### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

When adding a custom id to an apigateway V1 via tags in aws-cdk the id will be applied and deploying returns the url including the custom id (https://<custom-id>.execute-api.localhost.localstack.cloud:4566/prod/). Querying this url however will return a 404 response. 

The url generated when no custom id is provided works with issue.

### Expected Behavior

The custom id is applied and querying works with the url including the custom id.

### How are you starting LocalStack?

With the `localstack` script

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

localstack start -d

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)
*AWS CDK (python)*
```python
# test-stack.py
from aws_cdk import (
    Stack,
    aws_lambda,
    aws_apigateway as api_gateway,
    Tags,
)
from pathlib import Path
from constructs import Construct


class TestStack(Stack):
    def __init__(self, scope: Construct, construct_id: str, **kwargs) -> None:
        super().__init__(scope, construct_id, **kwargs)

        my_lambda = aws_lambda.Function(
            self,
            "test-lambda",
            code=aws_lambda.Code.from_asset("lambdas"),
            runtime=aws_lambda.Runtime.PYTHON_3_9,
            handler="test_lambda.handle",
        )

        api = api_gateway.RestApi(
            self,
            "Api",
            rest_api_name="apiName",
        )
        Tags.of(api).add(
            "_custom_id_", "myCustomId"
        )  # makes api id and therefore url static

        api.root.add_method(
            "GET", api_gateway.LambdaIntegration(my_lambda)  # type: ignore
        )

```
```python
# lambdas/test_lambda.py
def handle(event, context):
    return {"statusCode": 200, "body": {}}
```

Deploy outputs: https://myCustomId.execute-api.localhost.localstack.cloud:4566/prod/
Querying this url returns 404

![localstack-bug-postman](https://user-images.githubusercontent.com/48515433/201137013-0e0f1161-7818-427a-88d8-a12e9c2b2199.JPG)

### Environment

```markdown
- OS: Windows 10
- LocalStack: latest (10.11.2022)
- aws-cdk@2.44.0
```


### Anything else?

I found [#4499](https://github.com/localstack/localstack/issues/4499), but from the deploy output and awslocal it seems that the Api Gateway should have been created with the custom id but cannot be queried.  

---
Result without custom id:

![localstack-bug-postman-expected](https://user-images.githubusercontent.com/48515433/201140708-84f49aa2-cd3f-49e1-8947-9b6572941630.JPG)

invocation_context: ApiInvocationContext,
) -> ApiInvocationContext:
    
    values = (
        invocation_context.api_id,
        invocation_context.stage,
        invocation_context.path_with_query_string,
    )
    if all(values):
        return invocation_context
    
    if invocation_context.is_websocket_request():
        return invocation_context
    path = invocation_context.path
    headers = invocation_context.headers
    path_match = re.search(PATH_REGEX_USER_REQUEST, path)
    host_header = headers.get(HEADER_LOCALSTACK_EDGE_URL, "") or headers.get("Host") or ""
    host_match = re.search(HOST_REGEX_EXECUTE_API, host_header)
    test_invoke_match = re.search(PATH_REGEX_TEST_INVOKE_API, path)
    if path_match:
        api_id = path_match.group(1)
        stage = path_match.group(2)
        relative_path_w_query_params = "/%s" % path_match.group(3)
    elif host_match:
        api_id = extract_api_id_from_hostname_in_url(host_header)
        stage = path.strip("/").split("/")[0]