feat: sync notification badge + clarify cloud storage support

Notification system:
- When sync applies data (file folder, browser account, or sync code),
  ss_sync_notification is written to local storage with the source.
- Service worker catches it via storage.onChanged, shows a purple 'SYN'
  badge on the extension icon that persists until Options is opened, and
  fires a desktop notification ('Settings updated via sync folder — open
  Options to review').
- Clicking the desktop notification opens the Options page directly.
- On service worker wake, SYN badge is restored if the notification was
  not yet dismissed.
- Opening Options clears ss_sync_notification, resets the badge, and
  sends a sync:notification-seen message to the service worker.
- Added 'notifications' permission to both manifests.

Cloud storage clarity:
- Options page now explicitly lists that the folder sync works with any
  cloud storage that has a desktop sync client: Dropbox, OneDrive, Google
  Drive, iCloud Drive, Box, pCloud, Nextcloud, Synology Drive, etc.

https://claude.ai/code/session_01TKpSR9M8JgHLXCp5CeDsQP

src/options/options.js

@@ -96,6 +96,10 @@ document.addEventListener('DOMContentLoaded', async () => {
   });
 
   // --- File-based auto-sync ---
+  // Tell the service worker the user has seen any pending sync notification
+  api.runtime.sendMessage({ type: 'sync:notification-seen' }).catch(() => {});
+  await api.storage.local.remove('ss_sync_notification');
+
   await initFileSync();
 
   $('#btnPickSyncFolder').addEventListener('click', pickSyncFolder);
@@ -559,7 +563,7 @@ async function checkFileSyncUpdate() {
 
     const local = await SilentSendSync._getAllData();
     if (data.lastModified > (local.lastModified || 0)) {
-      await SilentSendSync._applyData(data);
+      await SilentSendSync._applyData(data, 'file');
       mappings = await Storage.getMappings();
       settings = await Storage.getSettings();
       $('#browserSync').checked = settings.browserSync === true;