Live Activity Launch Consistency

Nucleic-Session: 9D2EE9AB-2E44-485B-A196-54D250F9D89B
Co-authored-by: Nucleic <[email protected]>

NucleicRemote/NucleicRemote/Models/RemoteStore.swift

@@ -1584,6 +1584,32 @@ final class RemoteStore: ObservableObject {
         }
     }
 
+    /// Tell every capable, live host the current foreground state so it can pick the Live Activity
+    /// path: defer to the phone's own creation while foreground, or push-to-start the glance while
+    /// backgrounded (UX_IOS §5.3). De-duped per host against the value already sent; the set is
+    /// cleared by `setForegroundState` when the value flips, and a host that dropped re-learns it when
+    /// it returns (via the `didUpdate` re-sync). Gated on the dedicated capability bit — an older host
+    /// (even one advertising push-to-start) throws on the unknown `setForeground` tag.
+    private func syncForegroundState() {
+        foregroundSentTo = foregroundSentTo.filter { connections[$0]?.connectivity.isLive == true }
+        for (id, conn) in connections {
+            guard conn.connectivity.isLive, conn.capabilities.canReceiveForegroundState,
+                  !foregroundSentTo.contains(id) else { continue }
+            conn.send(.setForeground(isForeground))
+            foregroundSentTo.insert(id)
+        }
+    }
+
+    /// Record a foreground/background transition and push it to the hosts. No-op when unchanged so an
+    /// `inactive`↔`active` flutter (or a repeat call) doesn't re-notify; on a real flip it clears the
+    /// per-host dedup so `syncForegroundState` re-sends to everyone.
+    private func setForegroundState(_ foreground: Bool) {
+        guard isForeground != foreground else { return }
+        isForeground = foreground
+        foregroundSentTo.removeAll()
+        syncForegroundState()
+    }
+
     // MARK: - Demo simulator (offline, interactive)
     //
     // In demo mode there's no host, so writes can't go over the wire. Instead they mutate the