Can't get custom response headers middleware to work with Websocket connection

Traefik Traefik v2 (latest)
1

I'm struggling to get the headers middleware to work with a websocket connection, am I doing something wrong or is this not supported? Minimal example docker compose below.

version: "3.3"

services:

  traefik:
    image: "traefik:v2.7"
    container_name: "traefik"
    command:
      - "--api.insecure=true"
      - "--providers.docker=true"
      - "--providers.docker.exposedbydefault=false"
      - "--entrypoints.web.address=:80"
    ports:
      - "80:80"
      - "8080:8080"
    volumes:
      - "/var/run/docker.sock:/var/run/docker.sock:ro"
    labels:
      - "traefik.enable=true"
      - "traefik.http.middlewares.chickenheader.headers.customresponseheaders.chicken=tasty"

  whoami:
    image: "traefik/whoami"
    container_name: "simple-service"
    labels:
      - "traefik.enable=true"
      - "traefik.http.routers.whoami.rule=Host(`whoami.localhost`)"
      - "traefik.http.routers.whoami.entrypoints=web"
      - "traefik.http.routers.whoami.middlewares=chickenheader"

  websocket:
    image: elegantmonkeys/websockets-demo
    labels:
      - "traefik.enable=true"
      - "traefik.http.routers.websocket.rule=Host(`websocket.localhost`)"
      - "traefik.http.routers.websocket.entrypoints=web"
      - "traefik.http.routers.websocket.middlewares=chickenheader"

The header is set correctly for the whoami service:

HTTP/1.1 200 OK
Chicken: tasty
Content-Length: 815
Content-Type: text/plain; charset=utf-8
Date: Wed, 13 Jul 2022 10:10:21 GMT

But not for the websocket:

HTTP/1.1 101 Switching Protocols
Connection: Upgrade
Sec-Websocket-Accept: fh6cm5211R7WI6cIK8h50Cqfuew=
Sec-Websocket-Extensions: permessage-deflate
Upgrade: websocket

Many thanks.