Fix system notifications ignoring mention-only and default room settings.

Skip non-highlight events for Mentions/Default non-DM rooms so public chats stay quiet unless they should ping.

docs/handoff/features/background-notifications/HANDOFF.md

@@ -76,6 +76,7 @@ tauri.ts / electron main
 - Multiple runtimes: `isTauri`, `isElectron`, `isCapacitorNative` branch logic
 - Pusher registration races on fast login/logout
 - Android small icon: `ic_stat_paarrot` must exist in Android resources
+- Background wake (`MatrixSyncService`) must filter by push rules / unread_notifications; a push for one room used to notify for every new message in the sync batch
 
 ## Future work
 
@@ -91,3 +92,4 @@ tauri.ts / electron main
 
 - Constants: `PUSHER_APP_ID_BASE`, `PUSHER_STORAGE_PREFIX` in `backgroundSync.ts`
 - Logo assets: `paarrot.svg`, `paarrot-unread.svg`, `paarrot-highlight.svg` in `public/res/svg/`
+- Android notify filter: mute / mentions / default-room behavior lives in `MatrixSyncService.resolveRoomNotifyMode`

src/app/pages/client/ClientNonUIFeatures.tsx

@@ -378,6 +378,14 @@ function MessageNotifications() {
         return;
       }
 
+      // Match TitleBar / room bell settings: Default and Mentions rooms only notify on highlights.
+      const notificationType = getNotificationType(mx, room.roomId);
+      const isDm = mDirects.has(room.roomId);
+      const mentionsOnly =
+        notificationType === NotificationType.MentionsAndKeywords ||
+        (notificationType === NotificationType.Default && !isDm);
+      if (mentionsOnly && unreadInfo.highlight === 0) return;
+
       if (
         showNotifications &&
         ((isTauri() && !isElectron()) || isCapacitorNative() || notificationPermission('granted'))
@@ -399,7 +407,6 @@ function MessageNotifications() {
           messageBody = typeof content.body === 'string' ? content.body : undefined;
         }
         
-        const isDm = room.getJoinedMemberCount() === 2 && !room.isSpaceRoom();
         notify({
           roomName: room.name ?? 'Unknown',
           roomAvatar: avatarMxc
@@ -430,6 +437,7 @@ function MessageNotifications() {
     notify,
     selectedRoomId,
     useAuthentication,
+    mDirects,
   ]);
 
   return null;