feat(plex): P0 backend foundations — catalog model, config, client

Optional Plex module groundwork (design locked 2026-07-05): plays the LOCAL
physical file; Plex is metadata + optional watch-sync only.

- models + migration 0044: plex_libraries/plex_shows/plex_seasons/plex_items
  (playable leaf, ffprobe playability class, markers, weighted FTS search_vector)
  + plex_states (per-user watch state, mirrors video_states)
- sysconfig 'plex' group + config.py env defaults (server url/token[secret]/
  path-map/libraries/sync-interval/max-transcodes)
- app/plex/client.py (PlexClient httpx: server info, sections, items, metadata
  +markers, image) + app/plex/paths.py (Plex→local path map + file resolve)
- routes/plex.py admin POST /api/plex/test (verify connection + list sections)

backend/app/main.py

@@ -38,6 +38,7 @@ from app.routes import (
     messages,
     notifications,
     playlists,
+    plex as plex_routes,
     public as public_routes,
     quota,
     saved_views,
@@ -138,6 +139,7 @@ app.include_router(messages.router)
 app.include_router(channels.router)
 app.include_router(playlists.router)
 app.include_router(saved_views.router)
+app.include_router(plex_routes.router)
 app.include_router(downloads.router)
 app.include_router(downloads.admin_router)
 app.include_router(public_routes.router)