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/Plex.md

@@ -71,3 +71,7 @@ root runs as the `dank` user, and the deployer adopts the data root with
 3. The claim token is the identity of this server; document it in the host
    `.env`, never in this repo (secret rules apply). The token lives in
    `Preferences.xml` inside the RW data bind, preserved by the migration.
+4. **Cold container boot is slow.** PMS pre-binds 32400 and empty-replies
+   while the HTTP layer finishes loading; the first boot of a years-old
+   library took ~10 minutes (2026-09 cutover). The deployer gate now allows
+   600 s before failing; later boots are much faster (warm page cache).