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).

frontend/src/lib/plexPlayerHooks.ts

@@ -102,6 +102,16 @@ export function usePlexProgress(opts: {
     const onPauseFlush = () => flush(true);
     const video = videoRef.current;
     video?.addEventListener("pause", onPauseFlush);
+    // A seek is a settled position too (S2: Plex is the source of truth, so it must see the new spot
+    // right away, not up to 10s later). Debounced so scrubbing — many `seeked` events in a row — pushes
+    // just ONCE, once the user lands. `final=true` bypasses the backend's ≥10s push-throttle, which is
+    // exactly why the debounce lives here: it bounds a scrub to one immediate Plex timeline call.
+    let seekTimer: number | undefined;
+    const onSeekFlush = () => {
+      window.clearTimeout(seekTimer);
+      seekTimer = window.setTimeout(() => flush(true), 800);
+    };
+    video?.addEventListener("seeked", onSeekFlush);
     // Save on page unload too (F5/close/navigate): React effect cleanup does NOT run on a full reload,
     // so without this the resume point lags up to 10s — e.g. a seek right before F5 was lost. Uses a
     // keepalive beacon so the POST survives the unload (a final checkpoint — the user is leaving).
@@ -112,8 +122,10 @@ export function usePlexProgress(opts: {
     window.addEventListener("pagehide", onHide);
     return () => {
       window.clearInterval(iv);
+      window.clearTimeout(seekTimer);
       window.removeEventListener("pagehide", onHide);
       video?.removeEventListener("pause", onPauseFlush);
+      video?.removeEventListener("seeked", onSeekFlush);
       flush(true);
       // Back (unmount) persists the position server-side via flush(), but reopening the same item in
       // the SAME session read react-query's CACHED detail — whose position_seconds predated this