### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

We are using the `Authorization` header for routing purposes

```
 "authorization: AWS4-HMAC-SHA256 <...>"
```

https://github.com/localstack/localstack/issues/5770

### Expected Behavior

Use a custom header to avoid causing confusion with backend integrations

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

Run a custom HTTP integration without authorisation

### Environment

```markdown
- OS: 
- LocalStack:
```


### Anything else?

No
response = invocation_context.response
    integration = invocation_context.integration
    int_responses = integration.get("integrationResponses") or {}
    if not int_responses:
        return response
    entries = list(int_responses.keys())
    return_code = str(response.status_code)
    if return_code not in entries:
        if len(entries) > 1:
            LOG.info("Found multiple integration response status codes: %s", entries)
            return response
        return_code = entries[0]
    response_params = int_responses[return_code].get("responseParameters", {})
    for key, value in response_params.items():
        
        if str(key).lower().startswith("method.response.header."):
            header_name = key[len("method.response.header.") :]
            response.headers[header_name] = value.strip("'")
    return response
def set_api_id_stage_invocation_path(