### 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_
if not stage:
        return {}
    region_name = [name for name, region in apigateway_backends.items() if api_id in region.apis][0]
    api_gateway_client = aws_stack.connect_to_service("apigateway", region_name=region_name)
    try:
        response = api_gateway_client.get_stage(restApiId=api_id, stageName=stage)
        return response.get("variables")
    except Exception:
        LOG.info(f"Failed to get stage {stage} for api id {api_id}")
        return {}
def get_event_request_context(invocation_context: ApiInvocationContext):
    method = invocation_context.method
    path = invocation_context.path
    headers = invocation_context.headers
    integration_uri = invocation_context.integration_uri
    resource_path = invocation_context.resource_path
    resource_id = invocation_context.resource_id
    set_api_id_stage_invocation_path(invocation_context)
    relative_path, query_string_params = extract_query_string_params(
        path=invocation_context.path_with_query_string
    )
    api_id = invocation_context.api_id
    stage = invocation_context.stage
    source_ip = headers.get("X-Forwarded-For", ",").split(",")[-2].strip()
    integration_uri = integration_uri or ""
    account_id = integration_uri.split(":lambda:path")[-1].split(":function:")[0].split(":")[-1]
    account_id = account_id or TEST_AWS_ACCOUNT_ID
    domain_name = f"{api_id}.execute-api.{LOCALHOST_HOSTNAME}"