### 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)

assert parsed_body.get("queryStringParameters") == {"foo": "foo", "bar": ["bar", "baz"]}
        request_context = parsed_body.get("requestContext")
        source_ip = request_context["identity"].pop("sourceIp")
        assert re.match(r"^\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}$", source_ip)
        expected_path = "/" + self.TEST_STAGE_NAME + "/lambda/foo1"
        assert expected_path == request_context["path"]
        assert request_context.get("stageVariables") is None
        assert get_aws_account_id() == request_context["accountId"]
        assert resource.get("id") == request_context["resourceId"]
        assert self.TEST_STAGE_NAME == request_context["stage"]
        assert "python-requests/testing" == request_context["identity"]["userAgent"]
        assert "POST" == request_context["httpMethod"]
        assert "HTTP/1.1" == request_context["protocol"]
        assert "requestTimeEpoch" in request_context
        assert "requestTime" in request_context
        assert "requestId" in request_context
        
        headers = parsed_body.get("headers") or {}
        header_names = list(headers.keys())
        assert "Host" in header_names
        assert "Content-Length" in header_names
        assert "User-Agent" in header_names
        result = requests.delete(url, data=json.dumps(data))
        assert 204 == result.status_code
        
        body_msg = "🙀 - 参よ"
        result = requests.post(url, data=json.dumps({"return_raw_body": body_msg}))
        assert body_msg == to_str(result.content)
        # send 
        binary_msg = b"\xff \xaa \x11"