feat(plex): P1 backend — catalog sync + browse/search/show/image API

- app/plex/sync.py: full reconcile of enabled movie/show sections into plex_*
  (upsert by rating_key). Reuses Plex's own codec info to classify browser
  playability (direct/remux/transcode) — no ffprobe. Movies + episodes become
  playable leaves; shows/seasons mirrored for the drill-down.
- routes/plex.py: GET /libraries, /browse (FTS search + sort + paging, movie
  leaves or show cards), /show/{rk} (seasons+episodes, per-user state), /image
  (proxies Plex art, no duplication); admin POST /sync. All auth'd, demo-allowed.
- scheduler: plex_sync job (interval settings.plex_sync_interval_min).
- Verified against the real server: 2 libs, 3206 movies, 260 shows/961 seasons/
  14768 episodes synced in 13s; FTS search + drill-down work. Playability:
  ~1% direct, 89% remux, 6% transcode (informs P2/P3).

backend/app/sysconfig.py

@@ -82,7 +82,7 @@ SPECS: tuple[ConfigSpec, ...] = (
     ConfigSpec("plex_server_token", "str", "plex", "plex_server_token", secret=True),
     ConfigSpec("plex_path_map", "str", "plex", "plex_path_map"),
     ConfigSpec("plex_libraries", "str", "plex", "plex_libraries"),
-    ConfigSpec("plex_sync_interval_min", "int", "plex", "plex_sync_interval_min", min=5, max=100_000),
+    # (plex_sync_interval_min is tuned from the Scheduler dashboard, not here — it's a scheduler job.)
     ConfigSpec("plex_max_transcodes", "int", "plex", "plex_max_transcodes", min=0, max=16),
 )