Issue:
Bug: [FEATURE] Fix spell check



### Feature Description

Need to fix spell check in router

### Possible Implementation

Need to fix spell check in router

### 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 -->

- [ ] Bugfix
- [ ] New feature
- [ ] Enhancement
- [x] Refactoring
- [ ] Dependency updates
- [ ] Documentation
- [ ] CI/CD

## Description
<!-- Describe your changes in detail -->
- Fixed spell checks
- Added `routing_approach` field in routing events API response


### 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)?
-->
1. hit the routing analytics API
```
curl -H "api-key: dev_R5xpWKgvxcaxLcQateRbZKt8B9XkvqaPziIdwPHaPQrGTDTq5JRyncxPtOq9JNsj" "http://localhost:8080/analytics/v1/profile/routing_event_logs?type=Payment&payment_id=pay_evlgasQRCFOJplN3yWge"
```

Response - 

```
[
  {
    "merchant_id": "merchant_1748952604",
    "profile_id": "pro_SoNvSCTpaIDKRzkJqf59",
    "payment_id": "pay_evlgasQRCFOJplN3yWge",
    "routable_connectors": "Stripe:\"mca_rozlszQ8vn82sR6d42xe\"",
    "payment_connector": null,
    "request_id": "019735b4-19a5-7ed1-8efb-412f3d26f6e0",
    "flow": "Intelligent-router FetchSuccessRate",
    "url": "SuccessRateCalculator.FetchSuccessRate",
    "request": "{\"id\":\"pro_SoNvSCTpaIDKRzkJqf59\",\"params\":\"card\",\"labels\":[\"stripe:mca_rozlszQ8vn82sR6d42xe\"],\"config\":{\"min_aggregates_size\":5,\"default_success_rate\":100.0,\"specificity_level\":\"merchant\",\"exploration_percent\":20.0}}",
    "response": "{\"labels_with_score\":[{\"score\":100.0,\"label\":\"stripe:mca_rozlszQ8vn82sR6d42xe\"}],\"routing_approach\":\"exploitation\"}",
    "error": null,
    "status_code": 200,
    "created_at": "2025-06-03T12:11:25.008Z",
    "method": "Grpc",
    "routing_engine": "intelligent_router",
    "routing_approach": "Exploitation"
  },
  {
    "merchant_id": "merchant_1748952604",
    "profile_id": "pro_SoNvSCTpaIDKRzkJqf59",
    "payment_id": "pay_evlgasQRCFOJplN3yWge",
    "routable_connectors": "",
    "payment_connector": "Stripe:\"mca_rozlszQ8vn82sR6d42xe\"",
    "request_id": "019735b4-19a5-7ed1-8efb-412f3d26f6e0",
    "flow": "Intelligent-router UpdateSuccessRateWindow",
    "url": "SuccessRateCalculator.UpdateSuccessRateWindow",
    "request": "{\"id\":\"pro_SoNvSCTpaIDKRzkJqf59\",\"params\":\"card\",\"labels_with_status\":[{\"label\":\"stripe:mca_rozlszQ8vn82sR6d42xe\",\"status\":true}],\"config\":{\"max_aggregates_size\":8,\"current_block_threshold\":{\"duration_in_mins\":null,\"max_total_count\":5}},\"global_labels_with_status\":[{\"label\":\"stripe:mca_rozlszQ8vn82sR6d42xe\",\"status\":true}]}",
    "response": "{\"status\":\"window_updation_succeeded\"}",
    "error": null,
    "status_code": 200,
    "created_at": "2025-06-03T12:11:26.323Z",
    "method": "Grpc",
    "routing_engine": "intelligent_router",
    "routing_approach": null
  }
]
```


## 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:

1. hit the routing analytics API
```
curl -H "api-key: dev_R5xpWKgvxcaxLcQateRbZKt8B9XkvqaPziIdwPHaPQrGTDTq5JRyncxPtOq9JNsj" "http://localhost:8080/analytics/v1/profile/routing_event_logs?type=Payment&payment_id=pay_evlgasQRCFOJplN3yWge"
```

Response - 

```
[
  {
    "merchant_id": "merchant_1748952604",
    "profile_id": "pro_SoNvSCTpaIDKRzkJqf59",
    "payment_id": "pay_evlgasQRCFOJplN3yWge",
    "routable_connectors": "Stripe:\"mca_rozlszQ8vn82sR6d42xe\"",
    "payment_connector": null,
    "request_id": "019735b4-19a5-7ed1-8efb-412f3d26f6e0",
    "flow": "Intelligent-router FetchSuccessRate",
    "url": "SuccessRateCalculator.FetchSuccessRate",
    "request": "{\"id\":\"pro_SoNvSCTpaIDKRzkJqf59\",\"params\":\"card\",\"labels\":[\"stripe:mca_rozlszQ8vn82sR6d42xe\"],\"config\":{\"min_aggregates_size\":5,\"default_success_rate\":100.0,\"specificity_level\":\"merchant\",\"exploration_percent\":20.0}}",
    "response": "{\"labels_with_score\":[{\"score\":100.0,\"label\":\"stripe:mca_rozlszQ8vn82sR6d42xe\"}],\"routing_approach\":\"exploitation\"}",
    "error": null,
    "status_code": 200,
    "created_at": "2025-06-03T12:11:25.008Z",
    "method": "Grpc",
    "routing_engine": "intelligent_router",
    "routing_approach": "Exploitation"
  },
  {
    "merchant_id": "merchant_1748952604",
    "profile_id": "pro_SoNvSCTpaIDKRzkJqf59",
    "payment_id": "pay_evlgasQRCFOJplN3yWge",
    "routable_connectors": "",
    "payment_connector": "Stripe:\"mca_rozlszQ8vn82sR6d42xe\"",
    "request_id": "019735b4-19a5-7ed1-8efb-412f3d26f6e0",
    "flow": "Intelligent-router UpdateSuccessRateWindow",
    "url": "SuccessRateCalculator.UpdateSuccessRateWindow",
    "request": "{\"id\":\"pro_SoNvSCTpaIDKRzkJqf59\",\"params\":\"card\",\"labels_with_status\":[{\"label\":\"stripe:mca_rozlszQ8vn82sR6d42xe\",\"status\":true}],\"config\":{\"max_aggregates_size\":8,\"current_block_threshold\":{\"duration_in_mins\":null,\"max_total_count\":5}},\"global_labels_with_status\":[{\"label\":\"stripe:mca_rozlszQ8vn82sR6d42xe\",\"status\":true}]}",
    "response": "{\"status\":\"window_updation_succeeded\"}",
    "error": null,
    "status_code": 200,
    "created_at": "2025-06-03T12:11:26.323Z",
    "method": "Grpc",
    "routing_engine": "intelligent_router",
    "routing_approach": null
  }
]
```

Patch:
diff --git a/crates/analytics/src/routing_events/events.rs b/crates/analytics/src/routing_events/events.rs
index 27b2f251627..b6090a588d2 100644
--- a/crates/analytics/src/routing_events/events.rs
+++ b/crates/analytics/src/routing_events/events.rs
@@ -70,4 +70,5 @@ pub struct RoutingEventsResult {
     pub created_at: PrimitiveDateTime,
     pub method: String,
     pub routing_engine: String,
+    pub routing_approach: Option<String>,
 }
diff --git a/crates/api_models/src/routing.rs b/crates/api_models/src/routing.rs
index 46cd37bc68a..e416bf4bae9 100644
--- a/crates/api_models/src/routing.rs
+++ b/crates/api_models/src/routing.rs
@@ -1339,7 +1339,7 @@ pub struct LabelWithScoreEventResponse {
 #[serde(rename_all = "snake_case")]
 pub struct CalSuccessRateEventResponse {
     pub labels_with_score: Vec<LabelWithScoreEventResponse>,
-    pub routing_apporach: RoutingApproach,
+    pub routing_approach: RoutingApproach,
 }
 
 #[derive(Clone, Debug, Serialize, Deserialize)]
diff --git a/crates/router/src/core/payments/routing.rs b/crates/router/src/core/payments/routing.rs
index fa161efb212..219eef52073 100644
--- a/crates/router/src/core/payments/routing.rs
+++ b/crates/router/src/core/payments/routing.rs
@@ -2087,7 +2087,7 @@ pub async fn perform_success_based_routing(
                 "unable to calculate/fetch success rate from dynamic routing service",
             )?;
 
-        let event_resposne = api_routing::CalSuccessRateEventResponse {
+        let event_response = api_routing::CalSuccessRateEventResponse {
             labels_with_score: success_based_connectors
                 .labels_with_score
                 .iter()
@@ -2098,7 +2098,7 @@ pub async fn perform_success_based_routing(
                     },
                 )
                 .collect(),
-            routing_apporach: match success_based_connectors.routing_approach {
+            routing_approach: match success_based_connectors.routing_approach {
                 0 => api_routing::RoutingApproach::Exploration,
                 1 => api_routing::RoutingApproach::Exploitation,
                 _ => {
@@ -2113,8 +2113,8 @@ pub async fn perform_success_based_routing(
             },
         };
 
-        routing_event.set_response_body(&event_resposne);
-        routing_event.set_routing_approach(event_resposne.routing_apporach.to_string());
+        routing_event.set_response_body(&event_response);
+        routing_event.set_routing_approach(event_response.routing_approach.to_string());
 
         let mut connectors = Vec::with_capacity(success_based_connectors.labels_with_score.len());
         for label_with_score in success_based_connectors.labels_with_score {
diff --git a/crates/router/src/core/routing/helpers.rs b/crates/router/src/core/routing/helpers.rs
index 4798cce9b02..f568aff55b1 100644
--- a/crates/router/src/core/routing/helpers.rs
+++ b/crates/router/src/core/routing/helpers.rs
@@ -1452,7 +1452,7 @@ pub async fn push_metrics_with_update_window_for_contract_based_routing(
                     routing_events::RoutingEngine::IntelligentRouter,
                 );
 
-                let update_respose = client
+                let update_response = client
                     .update_contracts(
                         profile_id.get_string_repr().into(),
                         vec![request_label_info],
@@ -1474,7 +1474,7 @@ pub async fn push_metrics_with_update_window_for_contract_based_routing(
                     )?;
 
                 let event_response = routing_types::UpdateContractEventResponse {
-                        status: match update_respose.status {
+                        status: match update_response.status {
                             0 => routing_types::ContractUpdationStatusEventResponse::ContractUpdationSucceeded,
                             1 => routing_types::ContractUpdationStatusEventResponse::ContractUpdationFailed,
                             _ => {