web: add firebase push token registration and sync

web/src/app/App.tsx

@@ -7,6 +7,7 @@ import { ChatsPage } from "../pages/ChatsPage";
 import { useAuthStore } from "../store/authStore";
 import { useChatStore } from "../store/chatStore";
 import { useUiStore } from "../store/uiStore";
+import { ensureWebPushRegistration } from "../utils/firebasePush";
 import { applyAppearancePreferences, getAppPreferences } from "../utils/preferences";
 
 const PENDING_INVITE_TOKEN_KEY = "bm_pending_invite_token";
@@ -118,6 +119,13 @@ export function App() {
     })();
   }, [accessToken, me, joiningInvite, loadChats, setActiveChatId, showToast]);
 
+  useEffect(() => {
+    if (!accessToken || !me) {
+      return;
+    }
+    void ensureWebPushRegistration();
+  }, [accessToken, me]);
+
   useEffect(() => {
     if (!accessToken || !me || joiningInvite) {
       return;