Google tag gateway in GKE Gateway API

I’m implementing server side tagging for Google Tag Manager through my GKE Gateway API.

I was successfully able to configure server side tag manager in same domain and GET https://www.example.com/metrics/healthy to return OK. Below is my gateway configuration.

kind: Gateway
apiVersion: gateway.networking.k8s.io/v1
metadata:
  name: http-gateway
spec:
  gatewayClassName: gke-l7-global-external-managed
  listeners:
  - name: http
    protocol: HTTP
    port: 80
    allowedRoutes:
      kinds:
      - kind: HTTPRoute
      namespaces:
        from: Selector
        selector:
          matchLabels:
            otherInfra: httpToHttps
  - name: https
    protocol: HTTPS
    port: 443
    tls:
      mode: Terminate
      options:
        networking.gke.io/pre-shared-certs: http-ssl
  addresses:
  - type: NamedAddress
    value: gke-http
---
kind: HTTPRoute
apiVersion: gateway.networking.k8s.io/v1
metadata:
  name: nginx
spec:
  parentRefs:
  - name: http-gateway
  hostnames:
  - "www.example.com"
  rules:
  - backendRefs:
    - name: nginx
      port: 80
---
kind: HTTPRoute
apiVersion: gateway.networking.k8s.io/v1
metadata:
  name: metrics
spec:
  parentRefs:
  - name: http-gateway
  hostnames:
  - "www.example.com"
  rules:
  - matches:
    - path:
        type: PathPrefix
        value: /metrics
    backendRefs:
    - name: metrics
      port: 8080

Above configuration can forward all /metrics traffic to server side tag. Now to serve first-party “script” requests to Google servers, I’m following the below document (Serve scripts with a CDN).

https://developers.google.com/tag-platform/tag-manager/server-side/dependency-serving?option=cdn

It says:

  1. Collection path (e.g. /metrics) → Forwards events to your tagging server

  2. Script path (e.g. /scripts) → Forwards first-party script requests to Google servers

Step 1 is already completed. How can I achieve step 2? I followed the below document to setup Google tag gateway. But my Load Balancer created using GKE Gateway API. I cannot modify it in Google Cloud Console. But I was able to setup backend service (Internet NEG) mentioned in the document.

https://developers.google.com/tag-platform/tag-manager/gateway/setup-guide?setup=manual#setup-type

Is there a way I can link this backend with my Gateway API through HTTPRoute or any other resource?

Or is there any other way to achive this?