Issue:
Bug: [BUG] Fix contract updation for Contract routing



### Feature Description

We need to update the contract once it is not found in the dynamic routing service.


### Possible Implementation

The updation happening in the post-update tracker does not work when the payment goes through a different connector.
Need to set the contract when fetch fails.

### Have you spent some time checking if this feature request has been raised before?

- [x] I checked and didn't find a similar issue

### Have you read the Contributing Guidelines?

- [x] I have read the [Contributing Guidelines](https://github.com/juspay/hyperswitch/blob/main/docs/CONTRIBUTING.md)

### Are you willing to submit a PR?

Yes, I am willing to submit a PR!

Pull request description:
## Type of Change
<!-- Put an `x` in the boxes that apply -->

- [x] Bugfix
- [ ] New feature
- [ ] Enhancement
- [ ] Refactoring
- [ ] Dependency updates
- [ ] Documentation
- [ ] CI/CD

## Description
<!-- Describe your changes in detail -->
Fixed the contract updation when contract is not set in dynamo. If contract is not set, we'll set in the same flow.
This fixes an issue.

### Additional Changes

- [ ] This PR modifies the API contract
- [ ] This PR modifies the database schema
- [ ] This PR modifies application configuration/environment variables

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1. `config`
2. `crates/router/src/configs`
3. `loadtest/config`
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## Motivation and Context
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Why is this change required? What problem does it solve?
If it fixes an open issue, please link to the issue here.

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## How did you test it?
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Did you write an integration/unit/API test to verify the code changes?
Or did you test this change manually (provide relevant screenshots)?
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Same as https://github.com/juspay/hyperswitch/pull/6761
New error log - 
![image](https://github.com/user-attachments/assets/26b7f7c0-ac06-4d8c-9996-d08f4c5b74fb)



## Checklist
<!-- Put an `x` in the boxes that apply -->

- [x] I formatted the code `cargo +nightly fmt --all`
- [x] I addressed lints thrown by `cargo clippy`
- [ ] I reviewed the submitted code
- [ ] I added unit tests for my changes where possible


Testing:

Same as https://github.com/juspay/hyperswitch/pull/6761
New error log - 
![image](https://github.com/user-attachments/assets/26b7f7c0-ac06-4d8c-9996-d08f4c5b74fb)

Patch:
diff --git a/crates/external_services/src/grpc_client/dynamic_routing.rs b/crates/external_services/src/grpc_client/dynamic_routing.rs
index e34f721b30e..67069b9fe8b 100644
--- a/crates/external_services/src/grpc_client/dynamic_routing.rs
+++ b/crates/external_services/src/grpc_client/dynamic_routing.rs
@@ -32,9 +32,12 @@ pub enum DynamicRoutingError {
     #[error("Error from Dynamic Routing Server while perfrming success_rate analysis : {0}")]
     SuccessRateBasedRoutingFailure(String),
 
-    /// Error from Dynamic Routing Server while performing contract based routing
+    /// Generic Error from Dynamic Routing Server while performing contract based routing
     #[error("Error from Dynamic Routing Server while performing contract based routing: {0}")]
     ContractBasedRoutingFailure(String),
+    /// Generic Error from Dynamic Routing Server while performing contract based routing
+    #[error("Contract not found in the dynamic routing service")]
+    ContractNotFound,
     /// Error from Dynamic Routing Server while perfrming elimination
     #[error("Error from Dynamic Routing Server while perfrming elimination : {0}")]
     EliminationRateRoutingFailure(String),
diff --git a/crates/external_services/src/grpc_client/dynamic_routing/contract_routing_client.rs b/crates/external_services/src/grpc_client/dynamic_routing/contract_routing_client.rs
index b210d996bc0..ff16594ca6e 100644
--- a/crates/external_services/src/grpc_client/dynamic_routing/contract_routing_client.rs
+++ b/crates/external_services/src/grpc_client/dynamic_routing/contract_routing_client.rs
@@ -26,6 +26,8 @@ use crate::grpc_client::{self, GrpcHeaders};
 pub mod contract_routing {
     tonic::include_proto!("contract_routing");
 }
+pub use tonic::Code;
+
 use super::{Client, DynamicRoutingError, DynamicRoutingResult};
 /// The trait ContractBasedDynamicRouting would have the functions required to support the calculation and updation window
 #[async_trait::async_trait]
@@ -46,6 +48,7 @@ pub trait ContractBasedDynamicRouting: dyn_clone::DynClone + Send + Sync {
         label_info: Vec<LabelInformation>,
         params: String,
         response: Vec<RoutableConnectorChoiceWithStatus>,
+        incr_count: u64,
         headers: GrpcHeaders,
     ) -> DynamicRoutingResult<UpdateContractResponse>;
     /// To invalidates the contract scores against the id
@@ -90,9 +93,10 @@ impl ContractBasedDynamicRouting for ContractScoreCalculatorClient<Client> {
             .clone()
             .fetch_contract_score(request)
             .await
-            .change_context(DynamicRoutingError::ContractBasedRoutingFailure(
-                "Failed to fetch the contract score".to_string(),
-            ))?
+            .map_err(|err| match err.code() {
+                Code::NotFound => DynamicRoutingError::ContractNotFound,
+                _ => DynamicRoutingError::ContractBasedRoutingFailure(err.to_string()),
+            })?
             .into_inner();
 
         logger::info!(dynamic_routing_response=?response);
@@ -106,13 +110,18 @@ impl ContractBasedDynamicRouting for ContractScoreCalculatorClient<Client> {
         label_info: Vec<LabelInformation>,
         params: String,
         _response: Vec<RoutableConnectorChoiceWithStatus>,
+        incr_count: u64,
         headers: GrpcHeaders,
     ) -> DynamicRoutingResult<UpdateContractResponse> {
-        let labels_information = label_info
+        let mut labels_information = label_info
             .into_iter()
             .map(ProtoLabelInfo::foreign_from)
             .collect::<Vec<_>>();
 
+        labels_information
+            .iter_mut()
+            .for_each(|info| info.current_count += incr_count);
+
         let request = grpc_client::create_grpc_request(
             UpdateContractRequest {
                 id,
@@ -183,10 +192,14 @@ impl ForeignTryFrom<ContractBasedRoutingConfigBody> for CalContractScoreConfig {
 impl ForeignFrom<LabelInformation> for ProtoLabelInfo {
     fn foreign_from(config: LabelInformation) -> Self {
         Self {
-            label: config.label,
+            label: format!(
+                "{}:{}",
+                config.label.clone(),
+                config.mca_id.get_string_repr()
+            ),
             target_count: config.target_count,
             target_time: config.target_time,
-            current_count: 1,
+            current_count: u64::default(),
         }
     }
 }
diff --git a/crates/router/src/core/errors.rs b/crates/router/src/core/errors.rs
index d06ffea581f..215f262ea8b 100644
--- a/crates/router/src/core/errors.rs
+++ b/crates/router/src/core/errors.rs
@@ -400,8 +400,10 @@ pub enum RoutingError {
     ContractBasedRoutingConfigError,
     #[error("Params not found in contract based routing config")]
     ContractBasedRoutingParamsNotFoundError,
-    #[error("Unable to calculate contract score from dynamic routing service")]
-    ContractScoreCalculationError,
+    #[error("Unable to calculate contract score from dynamic routing service: '{err}'")]
+    ContractScoreCalculationError { err: String },
+    #[error("Unable to update contract score on dynamic routing service")]
+    ContractScoreUpdationError,
     #[error("contract routing client from dynamic routing gRPC service not initialized")]
     ContractRoutingClientInitializationError,
     #[error("Invalid contract based connector label received from dynamic routing service: '{0}'")]
diff --git a/crates/router/src/core/payments/routing.rs b/crates/router/src/core/payments/routing.rs
index cf5cd35fb98..e78861d4327 100644
--- a/crates/router/src/core/payments/routing.rs
+++ b/crates/router/src/core/payments/routing.rs
@@ -26,8 +26,9 @@ use euclid::{
 };
 #[cfg(all(feature = "v1", feature = "dynamic_routing"))]
 use external_services::grpc_client::dynamic_routing::{
-    contract_routing_client::{CalContractScoreResponse, ContractBasedDynamicRouting},
+    contract_routing_client::ContractBasedDynamicRouting,
     success_rate_client::{CalSuccessRateResponse, SuccessBasedDynamicRouting},
+    DynamicRoutingError,
 };
 use hyperswitch_domain_models::address::Address;
 use kgraph_utils::{
@@ -1599,19 +1600,57 @@ pub async fn perform_contract_based_routing(
         .change_context(errors::RoutingError::ContractBasedRoutingConfigError)
         .attach_printable("unable to fetch contract based dynamic routing configs")?;
 
-        let contract_based_connectors: CalContractScoreResponse = client
+        let contract_based_connectors_result = client
             .calculate_contract_score(
                 profile_id.get_string_repr().into(),
-                contract_based_routing_configs,
+                contract_based_routing_configs.clone(),
                 "".to_string(),
                 routable_connectors,
                 state.get_grpc_headers(),
             )
             .await
-            .change_context(errors::RoutingError::ContractScoreCalculationError)
             .attach_printable(
                 "unable to calculate/fetch contract score from dynamic routing service",
-            )?;
+            );
+
+        let contract_based_connectors = match contract_based_connectors_result {
+            Ok(resp) => resp,
+            Err(err) => match err.current_context() {
+                DynamicRoutingError::ContractNotFound => {
+                    let label_info = contract_based_routing_configs
+                        .label_info
+                        .ok_or(errors::RoutingError::ContractBasedRoutingConfigError)
+                        .attach_printable(
+                            "Label information not found in contract routing configs",
+                        )?;
+
+                    client
+                            .update_contracts(
+                                profile_id.get_string_repr().into(),
+                                label_info,
+                                "".to_string(),
+                                vec![],
+                                u64::default(),
+                                state.get_grpc_headers(),
+                            )
+                            .await
+                            .change_context(errors::RoutingError::ContractScoreUpdationError)
+                            .attach_printable(
+                                "unable to update contract based routing window in dynamic routing service",
+                            )?;
+                    return Err((errors::RoutingError::ContractScoreCalculationError {
+                        err: err.to_string(),
+                    })
+                    .into());
+                }
+                _ => {
+                    return Err((errors::RoutingError::ContractScoreCalculationError {
+                        err: err.to_string(),
+                    })
+                    .into())
+                }
+            },
+        };
 
         let mut connectors = Vec::with_capacity(contract_based_connectors.labels_with_score.len());
 
diff --git a/crates/router/src/core/routing/helpers.rs b/crates/router/src/core/routing/helpers.rs
index b8a7ee5dc1c..17edc50a30d 100644
--- a/crates/router/src/core/routing/helpers.rs
+++ b/crates/router/src/core/routing/helpers.rs
@@ -1036,11 +1036,7 @@ pub async fn push_metrics_with_update_window_for_contract_based_routing(
             );
 
             let request_label_info = routing_types::LabelInformation {
-                label: format!(
-                    "{}:{}",
-                    final_label_info.label.clone(),
-                    final_label_info.mca_id.get_string_repr()
-                ),
+                label: final_label_info.label.clone(),
                 target_count: final_label_info.target_count,
                 target_time: final_label_info.target_time,
                 mca_id: final_label_info.mca_id.to_owned(),
@@ -1056,6 +1052,7 @@ pub async fn push_metrics_with_update_window_for_contract_based_routing(
                         vec![request_label_info],
                         "".to_string(),
                         vec![],
+                        1,
                         state.get_grpc_headers(),
                     )
                     .await