tautulli healthcheck via curl; restore PublishPort; plex gate to 600s

- tautulli.container: HealthCmd switches to the repo's proven curl pattern
  (jellyfin unit) — quadlet's systemd-style value parsing mangles embedded
  double quotes; PublishPort=8181:8181 restored (a mis-aimed line edit
  replaced it; the PublishPort seam test caught the regression)
- deploy_plex readiness gate: 36x5s -> 120x5s; the 2026-09 cutover showed
  the first container boot of a years-old library runs ~10 min while PMS
  pre-binds 32400 and empty-replies; 180s failed the gate twice with a
  healthy, still-booting service

serverAppConfigs-docs/Dankserver/Tautulli.md

@@ -20,7 +20,7 @@ it; it talks to PMS over the appnet at `http://plex:32400`).
 | Port | `8181/tcp` published on `0.0.0.0` |
 | Network | `dankserver_appnet`, alias `tautulli` |
 | PMS URL | `http://plex:32400` — seeded into `config.ini` by the deployer on first start |
-| Health | in-container `python3` probe of `http://localhost:8181/home`, 30 s interval / 3 retries |
+| Health | in-container `curl -fs http://localhost:8181/home` probe, 30 s interval / 3 retries |
 | Deploy | `./scripts/deploy.sh dankserver --service tautulli` |
 | Docs | https://github.com/Tautulli/Tautulli/wiki |