### 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
"""Extract API ID 'id123' from URLs like https://id123.execute-api.localhost.localstack.cloud:4566"""
    match = re.match(HOST_REGEX_EXECUTE_API, hostname)
    api_id = match.group(1)
    return api_id
def invoke_rest_api_from_request(invocation_context: ApiInvocationContext):
    set_api_id_stage_invocation_path(invocation_context)
    try:
        return invoke_rest_api(invocation_context)
    except AuthorizationError as e:
        api_id = invocation_context.api_id
        return make_error_response("Not authorized to invoke REST API %s: %s" % (api_id, e), 403)
def invoke_rest_api(invocation_context: ApiInvocationContext):
    invocation_path = invocation_context.path_with_query_string
    raw_path = invocation_context.path or invocation_path
    method = invocation_context.method
    headers = invocation_context.headers
    
    authorize_invocation(invocation_context)
    extracted_path, resource = get_target_resource_details(invocation_context)
    if not resource:
        return make_error_response("Unable to find path %s" % invocation_context.path, 404)
    
    validator = RequestValidator(invocation_context, aws_stack.connect_to_service("apigateway"))
    if not validator.is_request_valid():
        return make_error_response("Invalid request body", 400)
    api_key_required = resource.get("resourceMethods", {}).get(method, {}).get("apiKeyRequired")