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/sysconfig.py

@@ -76,6 +76,14 @@ SPECS: tuple[ConfigSpec, ...] = (
     ConfigSpec("download_layout", "str", "downloads", "download_layout"),
     ConfigSpec("download_worker_concurrency", "int", "downloads", "download_worker_concurrency", min=1, max=16),
     ConfigSpec("sponsorblock_default", "bool", "downloads", "sponsorblock_default"),
+    # --- Plex integration (optional; local-file playback + Plex metadata) ---
+    ConfigSpec("plex_enabled", "bool", "plex", "plex_enabled"),
+    ConfigSpec("plex_server_url", "str", "plex", "plex_server_url"),
+    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),
+    ConfigSpec("plex_max_transcodes", "int", "plex", "plex_max_transcodes", min=0, max=16),
 )
 
 _BY_KEY: dict[str, ConfigSpec] = {s.key: s for s in SPECS}