desktop: syncs on its own — at launch, soon after an edit, every few minutes and on focus

Until now the only caller of the sync engine was the "Sync now" button. A worker
thread now owns every cycle (the button's included, so two never overlap):

- launch: one cycle as the app opens;
- edit: every 10s it reads a fingerprint of the pending set and sends when that
  moved. A fingerprint rather than "anything pending", because a rejected change
  stays pending and would otherwise be resent every tick forever;
- timer: a pull every 5 minutes with nothing to send;
- focus: at most once per 30s.

Failed automatic cycles back off (doubling from 10s to 5 minutes). A panicking
cycle counts as a failed one rather than ending the thread. Every cycle is
emitted as inkwell://synced: the board reloads when the pull changed something,
and the Sync screen shows the last automatic failure. No final push on quit;
the launch cycle sends whatever was left.

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

frontend/src/views/BoardView.vue

@@ -11,7 +11,7 @@ import EmptyState from "../components/EmptyState.vue";
 import FilterBar from "../components/FilterBar.vue";
 import NoteGrid from "../components/NoteGrid.vue";
 import NoteEditor from "../components/NoteEditor.vue";
-import { isDesktop, onCaptured, sync as syncBridge } from "../desktop/bridge";
+import { isDesktop, onCaptured, onSynced, sync as syncBridge } from "../desktop/bridge";
 
 const notes = useNotesStore();
 const config = useConfigStore();
@@ -233,15 +233,25 @@ onMounted(() => {
 // unregistered on the way out so a board that has been navigated away from does
 // not keep reloading itself.
 let stopCaptureListener: (() => void) | null = null;
+// The desktop syncs in the background (autosync.rs). A cycle that pulled something
+// changed SQLite under this board, so it reloads — only then, so the cycles that
+// change nothing (most of them) cost the board nothing.
+let stopSyncListener: (() => void) | null = null;
 onMounted(() => {
   void onCaptured(() => void reload()).then((stop) => {
     stopCaptureListener = stop;
   });
+  void onSynced((cycle) => {
+    if (cycle.changed) void reload();
+  }).then((stop) => {
+    stopSyncListener = stop;
+  });
 });
 
 onBeforeUnmount(() => {
   window.removeEventListener("keydown", onBoardKey);
   stopCaptureListener?.();
+  stopSyncListener?.();
   ui.boardCardFocused = false;
 });
 watch([currentView, currentLabel, facetKey], reload);