### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

IaC = CDK.

Attempting to connect an API-GW endpoint directly to EventBridge.

```
      const awsIntegration = new apigateway.AwsIntegration({
      service: 'events',
      action: 'PutEvents',
      integrationHttpMethod: 'POST',
      options: {
        credentialsRole: role,
        requestTemplates: {
          'application/json': requestTemplate,
        },
        passthroughBehavior: apigateway.PassthroughBehavior.NEVER,
        integrationResponses: [
          successResponse,
          serverErrorResponse,
          clientErrorResponse,
        ],
      },
    });
```

Receiving response:

```
    {
      statusCode: 400,
      data: {
        Type: 'User',
        message: `Error invoking integration for API Gateway ID '1z7ky5zzcb': API Gateway AWS integration action URI "arn:aws:apigateway:ap-southeast-2:events:action/PutEvents", method "GET" not yet implemented`,
        __type: 'InvalidRequest'
      }
    }
```

Similar to bug reported:

* https://github.com/localstack/localstack/issues/5508

### Expected Behavior

* 200 response
* Event created in relevant Eventbus

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

docker run localstack/localstack

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

Calling the API endpoint using axios from jest tests.

### Environment

```markdown
- OS: MacOS
- LocalStack: latest
```


### Anything else?

_No response_
request: Request, url_params: Dict[str, Any] = None
) -> ApiInvocationContext:
    """
    Converts an HTTP Request object into an ApiInvocationContext.
    :param request: the original request
    :param url_params: the parameters extracted from the URL matching rules
    :return: the ApiInvocationContext
    """
    if url_params is None:
        url_params = {}
    method = request.method
    
    
    path = request.environ.get("RAW_URI")
    data = restore_payload(request)
    headers = Headers(request.headers)
    
    x_forwarded_for = headers.getlist("X-Forwarded-For")
    x_forwarded_for.append(request.remote_addr)
    x_forwarded_for.append(request.host)
    headers["X-Forwarded-For"] = ", ".join(x_forwarded_for)
    
    headers[HEADER_LOCALSTACK_EDGE_URL] = request.host_url.strip("/")
    
    
    
    
    
    return ApiInvocationContext(method, path, data, headers, stage=url_params.get("stage"))
def convert_response(result: RequestsResponse) -> Response: