Sync fixes: clean seeks, clock offset, end of file, 2.5 min read-ahead (proto 6)

- User seeks are intercepted at the player (SyncPlayer), previewed
  locally, sent once 300 ms after the drag ends; own echoes are matched
  by seekSeq and never re-applied; the landed check can't reapply a
  stale target. 1 s position poll removed.
- ping/pong clock offset (min-RTT ClockSync); positions use server time.
- Reports carry duration; buffer gate is min(4 s, remaining - 2 s);
  new finished transport instead of a HELD stall at the end.
- cache/readahead 150 s, 256 MiB demuxer cache, pins read back.
- Resumed reports put a stale ready member back in the set; hello.resume
  takes over the old member after an unclean drop (no ghost).
- Docs: roadmap rendering findings (HW path works; shaders verified).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/desktop/test/state_diff_test.dart

@@ -156,4 +156,39 @@ void main() {
       expect(localPlayAllowed(state, ''), isFalse);
     });
   });
+
+  group('finished', () {
+    test('stops in place: pause, no seek to the end, no drift seeks', () {
+      final diff = StateDiff();
+      final t = DateTime.now().toUtc();
+      diff.diff(_state(eventId: 1, transport: 'playing', position: 100), 100, t);
+      final end = _state(eventId: 2, transport: 'finished', position: 120);
+      final actions = diff.diff(end, 119.4, t);
+      expect(actions.whereType<SeekAction>(), isEmpty);
+      expect(actions.whereType<TransportAction>().single.playing, isFalse);
+      // Far off and later: still nothing.
+      expect(diff.diff(end, 50, t.add(const Duration(seconds: 10))), isEmpty);
+    });
+
+    test('late joiner lands just before the end, paused', () {
+      final diff = StateDiff();
+      final actions = diff.diff(
+          _state(eventId: 5, transport: 'finished', position: 120), 0,
+          DateTime.now().toUtc());
+      expect(actions.whereType<SeekAction>().single.position, 119);
+      expect(actions.whereType<TransportAction>().single.playing, isFalse);
+    });
+  });
+
+  test('serverPositionAt extrapolates on the server clock', () {
+    final st = StateBroadcast(
+      eventId: 1,
+      transport: 'playing',
+      position: 10,
+      serverTime: DateTime.utc(2026, 1, 1, 12),
+      mediaId: 1,
+      members: const [],
+    );
+    expect(serverPositionAt(st, DateTime.utc(2026, 1, 1, 12, 0, 2, 500)), 12.5);
+  });
 }