Issue:
Bug: refactor(euclid): add logs for euclid routing





Pull request description:
## Type of Change
<!-- Put an `x` in the boxes that apply -->

- [ ] Bugfix
- [ ] New feature
- [ ] Enhancement
- [ ] Refactoring
- [ ] Dependency updates
- [ ] Documentation
- [ ] CI/CD

## Description
<!-- Describe your changes in detail -->
Added logs for routing engine.

### Additional Changes

- [ ] This PR modifies the API contract
- [ ] This PR modifies the database schema
- [ ] This PR modifies application configuration/environment variables

<!--
Provide links to the files with corresponding changes.

Following are the paths where you can find config files:
1. `config`
2. `crates/router/src/configs`
3. `loadtest/config`
-->


## Motivation and Context
<!--
Why is this change required? What problem does it solve?
If it fixes an open issue, please link to the issue here.

If you don't have an issue, we'd recommend starting with one first so the PR
can focus on the implementation (unless it is an obvious bug or documentation fix
that will have little conversation).
-->


## How did you test it?
<!--
Did you write an integration/unit/API test to verify the code changes?
Or did you test this change manually (provide relevant screenshots)?
-->
This PR only introduces logs, hence no testing is required.

## Checklist
<!-- Put an `x` in the boxes that apply -->

- [ ] I formatted the code `cargo +nightly fmt --all`
- [ ] I addressed lints thrown by `cargo clippy`
- [ ] I reviewed the submitted code
- [ ] I added unit tests for my changes where possible


Testing:

This PR only introduces logs, hence no testing is required.

Patch:
diff --git a/crates/router/src/core/payments.rs b/crates/router/src/core/payments.rs
index 0c0061e7918..44a4602ffa6 100644
--- a/crates/router/src/core/payments.rs
+++ b/crates/router/src/core/payments.rs
@@ -8103,6 +8103,7 @@ where
         .attach_printable("Invalid connector name received in 'routed_through'")?;
 
         routing_data.routed_through = Some(connector_name.clone());
+        logger::debug!("euclid_routing: predetermined connector present in attempt");
         return Ok(ConnectorCallType::PreDetermined(connector_data.into()));
     }
 
@@ -8122,6 +8123,7 @@ where
             .merchant_connector_id
             .clone_from(&mandate_connector_details.merchant_connector_id);
 
+        logger::debug!("euclid_routing: predetermined mandate connector");
         return Ok(ConnectorCallType::PreDetermined(connector_data.into()));
     }
 
@@ -8206,6 +8208,8 @@ where
                 }
             }
 
+            logger::debug!("euclid_routing: pre-routing connector present");
+
             let first_pre_routing_connector_data_list = pre_routing_connector_data_list
                 .first()
                 .ok_or(errors::ApiErrorResponse::IncorrectPaymentMethodConfiguration)?;
@@ -8269,6 +8273,7 @@ where
             .change_context(errors::ApiErrorResponse::InternalServerError)
             .attach_printable("Invalid connector name received")?;
 
+        logger::debug!("euclid_routing: straight through connector present");
         return decide_multiplex_connector_for_normal_or_recurring_payment(
             &state,
             payment_data,
@@ -8313,6 +8318,7 @@ where
             .attach_printable("failed eligibility analysis and fallback")?;
         }
 
+        logger::debug!("euclid_routing: single connector present in algorithm data");
         let connector_data = connectors
             .into_iter()
             .map(|conn| {
@@ -8400,7 +8406,7 @@ where
             Some(api::MandateTransactionType::RecurringMandateTransaction),
         )
         | (None, Some(_), None, Some(true), _) => {
-            logger::debug!("performing routing for token-based MIT flow");
+            logger::debug!("euclid_routing: performing routing for token-based MIT flow");
 
             let payment_method_info = payment_data
                 .get_payment_method_info()
@@ -8513,7 +8519,9 @@ where
                     .into(),
                 ))
             } else {
-                logger::error!("no eligible connector found for the ppt_mandate payment");
+                logger::error!(
+                    "euclid_routing: no eligible connector found for the ppt_mandate payment"
+                );
                 Err(errors::ApiErrorResponse::IncorrectPaymentMethodConfiguration.into())
             }
         }
@@ -8572,7 +8580,7 @@ where
             })
             .unwrap_or(false)
         {
-            logger::info!("using connector_mandate_id for MIT flow");
+            logger::info!("euclid_routing: using connector_mandate_id for MIT flow");
             if let Some(merchant_connector_id) = connector_data.merchant_connector_id.as_ref() {
                 if let Some(mandate_reference_record) = connector_mandate_details.clone()
                         .get_required_value("connector_mandate_details")
diff --git a/crates/router/src/core/payments/routing.rs b/crates/router/src/core/payments/routing.rs
index 19ddeb7f15f..a06b6140da4 100644
--- a/crates/router/src/core/payments/routing.rs
+++ b/crates/router/src/core/payments/routing.rs
@@ -441,6 +441,7 @@ pub async fn perform_static_routing_v1(
     Vec<routing_types::RoutableConnectorChoice>,
     Option<common_enums::RoutingApproach>,
 )> {
+    logger::debug!("euclid_routing: performing routing for connector selection");
     let get_merchant_fallback_config = || async {
         #[cfg(feature = "v1")]
         return routing::helpers::get_merchant_default_config(
@@ -459,6 +460,7 @@ pub async fn perform_static_routing_v1(
         id
     } else {
         let fallback_config = get_merchant_fallback_config().await?;
+        logger::debug!("euclid_routing: active algorithm isn't present, default falling back");
         return Ok((fallback_config, None));
     };
     let cached_algorithm = ensure_algorithm_cached_v1(
@@ -1038,6 +1040,7 @@ pub async fn perform_eligibility_analysis_with_fallback(
     eligible_connectors: Option<Vec<api_enums::RoutableConnectors>>,
     business_profile: &domain::Profile,
 ) -> RoutingResult<Vec<routing_types::RoutableConnectorChoice>> {
+    logger::debug!("euclid_routing: performing eligibility");
     let mut final_selection = perform_eligibility_analysis(
         state,
         key_store,
@@ -1072,7 +1075,7 @@ pub async fn perform_eligibility_analysis_with_fallback(
         .iter()
         .map(|item| item.connector)
         .collect::<Vec<_>>();
-    logger::debug!(final_selected_connectors_for_routing=?final_selected_connectors, "List of final selected connectors for routing");
+    logger::debug!(final_selected_connectors_for_routing=?final_selected_connectors, "euclid_routing: List of final selected connectors for routing");
 
     Ok(final_selection)
 }