Salut, j'utilise le Docker de Linuxserver.io aussi, voici un exemple de config (pas de Traefik ceci dit) :

docker run -d \
--name plexchris \
--restart always \
-p 32400:32400/tcp \
-p 33401:33401/tcp \
-p 3005:3005/tcp \
-p 8324:8324/tcp \
-p 32469:32469/tcp \
-p 1900:1900/udp \
-p 32410:32410/udp \
-p 32412:32412/udp \
-p 32413:32413/udp \
-p 32414:32414/udp \
-e PLEX_UID="0" \
-e PLEX_GID="0" \
-e TZ="Europe/Paris" \
-e PLEX_CLAIM="claim-abcd" \
-e ADVERTISE_IP="http://123.456.789.10:32400/" \
-h plex.domaine.tld \
-v /var/lib/vz/user/docker/plex:/config \
-v /tmp:/transcode \
-v /var/lib/vz/user/mnt/unionfs:/data \
--label=com.centurylinklabs.watchtower.enable=true \
plexinc/pms-docker:plexpass

Si j'ai bien suivi il te "manquerait" le claim et l'ip:port de publication du serveur Plex.
-e PLEX_CLAIM="claim-abcd" \
-e ADVERTISE_IP="http://123.456.789.10:32400/" \

Effectivement j'ai essayé de reproduire comme toi avec traefik et linuxserver, avec, et sans le claim!! Sans succés. Du coup je suis revenu à la bonne vieille méthode du tunnel et là ça a marché.
https://blog.microserum.net/index.php/2018/05/21/installation-de-plex-media-server-sous-linux/

Je te donne quand même mon docker compose

  plex:
    image: linuxserver/plex
    container_name: plex
    hostname: plex
    restart: unless-stopped
    labels:
      - traefik.enable=true
      - traefik.frontend.rule=Host:plex.domaine.pw
      - traefik.port=32400
      - traefik.docker.network=traefik_proxy
    environment:
      - PUID=1000
      - PGID=1000
      - TZ=Europe/Paris
    ports:
      - 32400:32400
    volumes:
      - /home/toto/docker/plex/config:/config
      - /dev/shm:/transcode
    networks:
      - proxy

Mon traefik.toml

defaultEntryPoints = ["https","http"]
InsecureSkipVerify = true

[api]
entryPoint = "traefik"
dashboard = true

[entryPoints]
  [entryPoints.http]
  address = ":80"
    [entryPoints.http.redirect]
    entryPoint = "https"
  [entryPoints.https]
  address = ":443"
    [entryPoints.https.tls]
    minVersion = "VersionTLS12"
    cipherSuites = [
      "TLS_ECDHE_RSA_WITH_CHACHA20_POLY1305",
      "TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384",
      "TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256",
      "TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256",
      "TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA",
      "TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA"
    ]
  [entryPoints.traefik]
  address = ":8080"

[acme]
email = ""
storage = "/etc/traefik/acme/acme.json"
entryPoint = "https"
onHostRule = true
onDemand = false
  [acme.httpChallenge]
  entryPoint = "http"

[docker]
endpoint = "unix:///var/run/docker.sock"
domain = "domaine.pw"
watch = true
exposedbydefault = false

et mon docker compose traefik

  traefik:
    image: traefik
    container_name: proxy_traefik
    restart: unless-stopped
    hostname: traefik
    labels:
      - traefik.enable=true
      - traefik.frontend.rule=Host:traefik.domaine.pw
      - traefik.frontend.auth.basic=toto:$$apr1$$Lfytr9.7$$/44xKrdPV9TOxYL/tHIgE0
      - traefik.port=8080
      - traefik.docker.network=traefik_proxy
    volumes:
      - /var/run/docker.sock:/var/run/docker.sock:ro
      - /opt/seedbox/docker/traefik/traefik.toml:/traefik.toml:ro
      - /opt/seedbox/docker/traefik/letsencrypt/certs:/etc/traefik/acme:rw
      - /var/log/traefik:/var/log
    ports:
      - "80:80"
      - "443:443"
    networks:
      - proxy