### Is there an existing issue for this?

- [X] I have searched the existing issues and read the documentation

### Question

Using a websocket apigatewayv2 in localstack and i need to change the body of the request e.g. add the connectionid, which is something i can do with a HTTP integration on the AWS gateway, however when I try this with localstack i receive the following error "Unsupported integration type "HTTP" for Websocket API ID" and then prints the ID of the API, if this feature is not enabled then how should we test the actual API where the connectionId and other things are added to the request body

### Anything else?

_No response_
"""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)
    api_key_required = resource.get("resourceMethods", {}).get(method, {}).get("apiKeyRequired")