### 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_
for i in range(0, len(conditions), 2):
        if conditions[i] == "<" and not (value < conditions[i + 1]):
            return False
        if conditions[i] == ">" and not (value > conditions[i + 1]):
            return False
        if conditions[i] == "<=" and not (value <= conditions[i + 1]):
            return False
        if conditions[i] == ">=" and not (value >= conditions[i + 1]):
            return False
    return True
def check_valid_numeric_content_base_rule(list_of_operators):
    if len(list_of_operators) > 4:
        return False
    if "=" in list_of_operators:
        return False
    if len(list_of_operators) > 2:
        upper_limit = None
        lower_limit = None
        for index in range(len(list_of_operators)):
            if not isinstance(list_of_operators[index], int) and "<" in list_of_operators[index]:
                upper_limit = list_of_operators[index + 1]
            if not isinstance(list_of_operators[index], int) and ">" in list_of_operators[index]:
                lower_limit = list_of_operators[index + 1]
            if upper_limit and lower_limit and upper_limit < lower_limit:
                return False
            index = index + 1
    return True
def filter_event_with_content_base_parameter(pattern_value: list, event_value: str | int):