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/routes/plex/playback.py

@@ -3,6 +3,7 @@
 import hashlib
 import os
 import tempfile
+import threading
 from datetime import datetime, timezone
 
 import httpx
@@ -155,6 +156,29 @@ _PROGRESS_MIN_S = 5
 
 _FINISH_MARGIN_S = 30
 
+# S2 write-back throttle: the resume position is now pushed to Plex on the periodic (non-final)
+# checkpoint too — not only on the final pause/unmount flush — so Plex (the source of truth) stays
+# current in near-real-time. To keep a single watch from spraying `/:/timeline` calls, a push is
+# rate-limited to at most one per item per user every _PUSH_THROTTLE_S seconds; a `final` checkpoint
+# (pause / seek / stop) always pushes immediately and resets the window. This is an in-memory, single-
+# process rate-limiter (the deployment is one FastAPI process): after a restart the map is empty, so at
+# most one extra push happens on the first checkpoint — harmless. It is NOT durable domain state.
+_PUSH_THROTTLE_S = 10
+_last_push_at: dict[tuple[int, int], datetime] = {}
+_push_throttle_lock = threading.Lock()
+
+
+def _should_push_resume(user_id: int, item_id: int, now: datetime, final: bool) -> bool:
+    """Whether to mirror this resume checkpoint to Plex now. `final` always pushes; a periodic tick
+    pushes only when ≥_PUSH_THROTTLE_S has elapsed since the last push for this (user, item). Records
+    `now` as the last-push time whenever it returns True so the window is measured from the real push."""
+    with _push_throttle_lock:
+        last = _last_push_at.get((user_id, item_id))
+        if final or last is None or (now - last).total_seconds() >= _PUSH_THROTTLE_S:
+            _last_push_at[(user_id, item_id)] = now
+            return True
+        return False
+
 
 @router.get("/person-image")
 def person_image(u: str, request: Request) -> Response:
@@ -232,9 +256,10 @@ def item_progress(
 ) -> dict:
     """Checkpoint the resume position while playing (near the end → mark watched + clear it).
 
-    `final` (sent on the pause/pagehide/unmount flush, not the periodic 10s checkpoint) is what
-    debounces the Plex resume push: we mirror the settled position to Plex only on a final flush, so
-    a single watch doesn't spray `/:/timeline` calls at the server every 10 seconds."""
+    S2 write-back: the resume position is mirrored to Plex (the source of truth) on the periodic
+    checkpoint too, not only on the final flush — throttled to ≥_PUSH_THROTTLE_S per item (see
+    `_should_push_resume`). `final` (sent on pause / seek / pagehide / unmount) pushes immediately and
+    resets the throttle window, so Plex sees a settled position the instant the user pauses or seeks."""
     it = item_or_404(db, rating_key)
     position = max(0, int(body.position_seconds))
     duration = int(body.duration_seconds)
@@ -280,10 +305,13 @@ def item_progress(
         db.add(st)
     st.position_seconds = position
     st.progress_updated_at = now
-    if final:
+    push_now = _should_push_resume(user.id, it.id, now, final)
+    if push_now:
+        # Mark dirty before the (background) push so the reconcile knows to re-push if it fails, and so
+        # `push_state_to_plex` can settle synced_to_plex once Plex confirms.
         st.synced_to_plex = False
     db.commit()
-    if final:
+    if push_now:
         _push_watch(
             background,
             db,