### 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_
from localstack.utils import common
from localstack.utils.analytics import event_publisher
from localstack.utils.aws import aws_responses, aws_stack
from localstack.utils.aws.aws_responses import (
    LambdaResponse,
    flask_to_requests_response,
    parse_query_string,
    request_response_stream,
    requests_response,
)
from localstack.utils.aws.request_context import MARKER_APIGW_REQUEST_REGION, THREAD_LOCAL
from localstack.utils.common import camel_to_snake_case, json_safe, long_uid, to_bytes, to_str
from localstack.utils.http_utils import add_query_params_to_url
LOG = logging.getLogger(__name__)
TARGET_REGEX_S3_URI = (
    r"^arn:aws:apigateway:[a-zA-Z0-9\-]+:s3:path/(?P<bucket>[^/]+)/(?P<object>.+)$"
)
PATH_REGEX_USER_REQUEST = (
    r"^/restapis/([A-Za-z0-9_\-]+)/([A-Za-z0-9_\-]+)/%s/(.*)$" % PATH_USER_REQUEST
)
HOST_REGEX_EXECUTE_API = (
    r"(?:.*://)?([a-zA-Z0-9-]+)\.execute-api\.(%s|([^\.]+)\.amazonaws\.com)(.*)"
    % LOCALHOST_HOSTNAME
)
REQUEST_TIME_DATE_FORMAT = "%d/%b/%Y:%H:%M:%S %z"
class ApiGatewayVersion(Enum):
    V1 = "v1"
    V2 = "v2"
InvocationPayload = Union[Dict, str, bytes]
class AuthorizationError(Exception):