Push Notification Live Activity Redundancy

Nucleic-Session: 73687ED9-C11C-438C-832B-979332B73893
Co-authored-by: Nucleic <[email protected]>

NucleicRemote/NucleicRemote/Models/RemoteStore.swift

@@ -698,9 +698,16 @@ final class RemoteStore: ObservableObject {
                !self.openApprovals.contains(where: { $0.id == req.id }) {
                 self.openApprovals.append(req)
             }
-            // Post for any host; the router suppresses the banner if the user is on this session.
+            // Prefer the Live Activity: when backgrounded with a glance on screen, the glance itself
+            // carries the approval (its inline Allow/Deny) and alerts (sound/haptic) via the local
+            // update path — so don't also post a banner. In-app the glance isn't the surface (it
+            // doesn't show over the app that controls it), so the banner is; and if there's no glance
+            // at all (Live Activities off) the banner is the only surface, so keep it as the fallback.
+            // willPresent still suppresses the banner when the user is already on this session.
+            if isForeground || !LiveActivityManager.shared.hasLiveActivity {
                 NotificationRouter.shared.postApproval(req, sessionTitle: title)
             }
+        }
         cb.approvalResolved = { [weak self] resolved in
             guard let self else { return }
             self.openApprovals.removeAll { $0.id == resolved.id }