Sticky session with externalname service in kubernetes

Traefik Traefik v3 (latest)
1

I've created an externalname service and an ingressroute that serves two proxmox nodes:

---
apiVersion: v1
kind: Service
metadata:
  name: proxmox
  namespace: external-system
spec:
  type: ExternalName
  sessionAffinity: None
  externalName: proxmox.my.domain
---
apiVersion: traefik.io/v1alpha1
kind: IngressRoute
metadata:
  name: proxmox-proxy
  namespace: external-system
spec:
  entryPoints:
    - websecure
  routes:
    - kind: Rule
      match: Host(`proxmox.np.my.domain`)
      services:
        - healthCheck:
            interval: 10s
            path: /api2/json/access/domains
            timeout: 3s
          name: proxmox
          port: 8006
          scheme: https
          serversTransport: selfsigned
          sticky:
            cookie:
              name: StickyCookie
  tls: {}

The nslookup command result is:

nslookup proxmox
Server:  UnKnown
Address:  192.168.0.1

Name:    proxmox.my.domain
Addresses:  192.168.0.17
          192.168.0.13

The load balancing works as expected.
The proxmox nodes, when performing authentication, expects the server that initiated the oauth2 redirect to be the same one receiving the authorization code response redirect.
I enabled sticky session in the ingressroute, I can see the cookie being set, but the sticky session doesn't work. Both nodes are responding to requests.
I'm not sure if it helps or not but the sticky cookie value is 63832e04188372cc.

Is this scenario supported?

Thanks