### 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)

abs_path = "/test" if base_path_type == "ignore" else "/base/test"
        resource = [res for res in rs["items"] if res["path"] == abs_path][0]
        assert "GET" in resource["resourceMethods"]
        assert "requestParameters" in resource["resourceMethods"]["GET"]
        assert {"integration.request.header.X-Amz-Invocation-Type": "'Event'"} == resource[
            "resourceMethods"
        ]["GET"]["requestParameters"]
        url = path_based_url(api_id=rest_api_id, stage_name="dev", path=abs_path)
        response = requests.get(url)
        assert 200 == response.status_code
        
        spec_file = load_file(TEST_IMPORT_REST_API_FILE)
        rest_api_id, _, _ = import_apigw(body=spec_file, parameters=api_params)
        rs = apigateway_client.get_resources(restApiId=rest_api_id)
        resources = rs["items"]
        assert 3 == len(resources)
        paths = [res["path"] for res in resources]
        assert "/" in paths
        assert "/pets" in paths
        assert "/pets/{petId}" in paths
    def test_step_function_integrations(self, create_rest_apigw, apigateway_client):
        sfn_client = aws_stack.create_external_boto_client("stepfunctions")
        lambda_client = aws_stack.create_external_boto_client("lambda")
        state_machine_name = f"test-{short_uid()}"
        state_machine_def = {
            "Comment": "Hello World example",
            "StartAt": "step1",
            "States": {
                "step1": {"Type": "Task", "Resource": "__tbd__", "End": True},
            },