feat(plex): Plex-authoritative watch-sync — resume write-back + faster pull (S2)

Make Plex the source of truth for watch state:

- Write-back during playback: item_progress now pushes the resume position to
  Plex on the periodic checkpoint too (not only the final flush), throttled to
  one push per item every ~10s (in-memory, single-process rate limiter). The FE
  now also fires an immediate (debounced) push on seek.
- Faster incremental pull: 30 → 15 min (plex_watch_sync_interval_min).
- Plex-authoritative pull: _pull_apply resolves a genuine divergence to Plex's
  state instead of last-write-wins; the _same_state + synced_to_plex short-circuit
  still prevents a freshly-pushed row from bouncing. Removed the now-unused
  _LWW_TOLERANCE_S / _sift_ts.

Tests: 5 new in test_plex_watch_sync.py (Plex-wins resume/watched, no-bounce,
throttle final vs periodic).

backend/app/config.py

@@ -232,7 +232,9 @@ class Settings(BaseSettings):
     plex_sync_interval_min: int = 360
     # How often the incremental Plex→Siftlode watch-state reconcile runs, in minutes (Phase C):
     # a cheap history + on-deck pull plus a re-push of any states that failed their immediate push.
-    plex_watch_sync_interval_min: int = 30
+    # 15 min (S2): with Plex now the source of truth (prompt write-back on the ~10s checkpoint +
+    # Plex-authoritative pull), a faster incremental pull keeps Siftlode close to Plex-side changes.
+    plex_watch_sync_interval_min: int = 15
     # How often the FULL watch-state reconcile runs, in minutes (Phase C). A whole-section rescan
     # that catches what the incremental history feed can't — notably an un-watch done on the Plex
     # side — so it runs far less often (daily) than the incremental pass.