### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Reproducible with https://github.com/localstack/localstack-terraform-samples/tree/master/apigatewayv2-http-referer-header

Describe here https://github.com/localstack/localstack/issues/5833

### Expected Behavior

Use of the `Referer` header should be consistent across method resources.

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

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

    docker run localstack/localstack

Run the example https://github.com/localstack/localstack-terraform-samples/tree/master/apigatewayv2-http-referer-header


### Environment

```markdown
- OS: 
- LocalStack:
```


### Anything else?

_No response_
if not self.service_manager.exists(api):
            raise HTTPErrorResponse("no provider exists for service %s" % api, code=500)
        try:
            self.service_manager.require(api)
        except Exception as e:
            raise HTTPErrorResponse("failed to get service for %s: %s" % (api, e), code=500)
def do_forward_request(api, method, path, data, headers, port=None):
    if config.FORWARD_EDGE_INMEM:
        result = do_forward_request_inmem(api, method, path, data, headers, port=port)
    else:
        result = do_forward_request_network(port, method, path, data, headers)
    if hasattr(result, "status_code") and int(result.status_code) >= 400 and method == "OPTIONS":
        
        return 200
    return result
def get_handler_for_api(api, headers):