k8s Gateway does (virtually?) not receive an IP address

I posted this question already. Or at least I thought I did. Maybe there was a communication issue, maybe something else. Gonna try again...

I'm trying to run RKE2 v1.34.9 (which comes with Traefik 3.7.13) with PureLB and Gateway API-only. Everything works except one thing. The gateway resource does not show an IP address:

kubectl get gateway -A
NAMESPACE     NAME      CLASS     ADDRESS   PROGRAMMED   AGE
kube-system   traefik   traefik             True         40h

Traefik if deployed without creating a managed gateway:

ingressClass:
  enabled: false

gateway:
  enabled: false   # don't create a default gateway

providers:
  kubernetesIngress:
    enabled: false
  kubernetesGateway:
    enabled: true

tlsStore:          # configure a default TLS certificate here
  default:
    defaultCertificate:
      secretName: rancher-guest-tls

The LB service looks like:

apiVersion: v1
kind: Service
metadata:
  labels:
    app.kubernetes.io/name: rke2-traefik
    app.kubernetes.io/instance: rke2-traefik-kube-system
  name: rke2-traefik-controller
  namespace: kube-system
spec:
  type: LoadBalancer
  ports:
    - name: http
      port: 80
      protocol: TCP
      targetPort: web
    - name: https
      port: 443
      protocol: TCP
      targetPort: websecure
  selector:
    app.kubernetes.io/instance: rke2-traefik-kube-system
    app.kubernetes.io/name: rke2-traefik

The result is:

kubectl get svc -A|grep Load
kube-system     rke2-traefik-controller                                           LoadBalancer   10.43.135.24    10.1.1.1   80:31791/TCP,443:31512/TCP   96s

Now I deployed the Traefik whoami app. With a Gateway and HTTPRoute like this

---
apiVersion: gateway.networking.k8s.io/v1
kind: Gateway
metadata:
  name: traefik
  namespace: kube-system
spec:
  gatewayClassName: traefik
  listeners:
    - name: http
      protocol: HTTP
      port: 8000
      allowedRoutes:
        namespaces:
          from: All
    - name: https
      protocol: HTTPS
      port: 8443
      tls:
        mode: Terminate
        certificateRefs:
          - name: rancher-guest-tls
            namespace: kube-system
      allowedRoutes:
        namespaces:
          from: All
---
apiVersion: gateway.networking.k8s.io/v1
kind: HTTPRoute
metadata:
  name: whoami-http
  namespace: default
spec:
  parentRefs:
    - name: traefik
      sectionName: http
      kind: Gateway
      namespace: kube-system
  hostnames:
    - <some-test-domain-name>
  rules:
    - filters:
        - type: RequestRedirect
          requestRedirect:
            scheme: https
---
apiVersion: gateway.networking.k8s.io/v1
kind: HTTPRoute
metadata:
  name: whoami-https
  namespace: default
spec:
  parentRefs:
    - name: traefik
      sectionName: https
      kind: Gateway
      namespace: kube-system
  hostnames:
    - <some-test-domain-name>
  rules:
    - matches:
        - path:
            type: PathPrefix
            value: /
      backendRefs:
        - name: whoami
          namespace: default
          port: 80

everything is working as expected. The whoami app is reachable over the LB IP, the HTTP URL is redirected, the HTTPS URL works. But still the Gateway does not show an IP address.

Why? Is there anything wrong with the configuration? How to debug? Any hints are highly appreciated.