### 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_
r"^{}".format(element_value.get(nested_key)), event_value
                    ):
                        return True
    return False
def handle_prefix_filtering(event_pattern, value):
    for element in event_pattern:
        if isinstance(element, (int, str)):
            if str(element) == str(value):
                return True
            if element in value:
                return True
        elif isinstance(element, dict) and "prefix" in element:
            if value.startswith(element.get("prefix")):
                return True
        elif isinstance(element, dict) and "anything-but" in element:
            if element.get("anything-but") != value:
                return True
        elif "numeric" in element:
            return handle_numeric_conditions(element.get("numeric"), value)
        elif isinstance(element, list):
            if value in list:
                return True
    return False
def identify_content_base_parameter_in_pattern(parameters) -> bool:
    return any(
        list(param.keys())[0] in CONTENT_BASE_FILTER_KEYWORDS
        for param in parameters
        if isinstance(param, dict)
    )
def get_two_lists_intersection(lst1: List, lst2: List) -> List: