### 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)

base_path = (resolved_schema.get("basePath") or "").strip("/").split("/")[0]
        base_path = f"/{base_path}" if base_path else ""
    for path in resolved_schema.get("paths", {}):
        get_or_create_path(base_path + path, base_path=base_path)
    policy = resolved_schema.get("x-amazon-apigateway-policy")
    if policy:
        policy = json.dumps(policy) if isinstance(policy, dict) else str(policy)
        rest_api.policy = policy
    minimum_compression_size = resolved_schema.get("x-amazon-apigateway-minimum-compression-size")
    if minimum_compression_size is not None:
        rest_api.minimum_compression_size = int(minimum_compression_size)
    endpoint_config = resolved_schema.get("x-amazon-apigateway-endpoint-configuration")
    if endpoint_config:
        if endpoint_config.get("vpcEndpointIds"):
            endpoint_config.setdefault("types", ["PRIVATE"])
        rest_api.endpoint_configuration = endpoint_config
    return rest_api
def get_target_resource_details(invocation_context: ApiInvocationContext) -> Tuple[str, Dict]:
    """Look up and return the API GW resource (path pattern + resource dict) for the given invocation context."""
    path_map = get_rest_api_paths(
        rest_api_id=invocation_context.api_id, region_name=invocation_context.region_name
    )
    relative_path = invocation_context.invocation_path.rstrip("/") or "/"
    try:
        extracted_path, resource = get_resource_for_path(path=relative_path, path_map=path_map)
        invocation_context.resource = resource
        return extracted_path, resource
    except Exception:
        return None, None
def get_target_resource_method(invocation_context: ApiInvocationContext) -> Optional[Dict]: