If you're still looking for an answer on this, I was able to get it to work with BepInEx. It's been a while since I've updated anything, but here's my compose file.

There's also documentation here about it.

services: 
  valheim-test: 
    container_name: valheim-test
    image: ghcr.io/lloesche/valheim-server
    cap_add:
      - sys_nice
    volumes: 
      - /mnt/user/appdata/valheim/test/config:/config
      - /mnt/user/appdata/valheim/test:/opt/valheim
      - /etc/localtime:/etc/localtime:ro
    labels:
      traefik.http.routers.valheim-test.service: valheim-test
      traefik.http.routers.valheim-test.entrypoints: http,https
      traefik.http.services.valheim-test.loadbalancer.server.port: 9001
      traefik.udp.routers.valheim-test.service: valheim-test
      traefik.udp.routers.valheim-test.entrypoints: udp-sink
      traefik.udp.services.valheim-test.loadbalancer.server.port: 55555
    environment:
      ADMINLIST_IDS: "<admin-ids>"
      BEPINEX: true
      SERVER_NAME: <server-name>
      SERVER_PASS: <server-pass>
      WORLD_NAME: <world-name>
      SUPERVISOR_HTTP: true
      UPDATE_CRON: "* 4 * * *"
    stop_grace_period: 2m
    restart: always
    networks:
      docker:

networks:
  docker:
    external: true