Push Notification Live Activity Redundancy

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

NucleicRemote/NucleicRemote/LiveActivityManager.swift

@@ -24,6 +24,18 @@ final class LiveActivityManager {
 
     private var activity: Activity<NucleicSessionAttributes>?
 
+    /// Whether an aggregate glance is currently on screen — `RemoteStore` checks this to decide
+    /// whether to fall back to a banner (no glance ⇒ the banner is the only surface).
+    var hasLiveActivity: Bool { activity != nil }
+
+    /// Whether the app is foreground, mirrored from `RemoteStore` (its `isForeground`). Drives where
+    /// a "needs you" arrival is announced: **foreground** the app UI / a banner does it, so the glance
+    /// updates silently; **backgrounded** there's no banner (we prefer the glance), so the update
+    /// itself carries an `AlertConfiguration` (sound/haptic). Starts `true` — `onAppear` runs
+    /// foreground; the background adopt path flips it. Mirrors the host's connected-vs-away gate for
+    /// the pushed glance, but for the still-connected phone whose own socket is alive.
+    var foreground = true
+
     /// The last content we pushed. Updates that don't change it are skipped so we don't spend
     /// ActivityKit's update budget on no-ops — `sync` fires on every host message (dashboard,
     /// connectivity, pong, diff ticks…), most of which leave the aggregate identical. Burning the