Live Activity Launch Consistency

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

NucleicRemote/NucleicRemote/Models/RemoteStore.swift

@@ -1511,6 +1511,14 @@ final class RemoteStore: ObservableObject {
     private var pushToStartToken: String?
     /// Host ids that already have the current push-to-start token (mirrors `liveActivitySentTo`).
     private var pushToStartSentTo: Set<String> = []
+    /// Whether the app is currently foreground. Reported to capable Macs (`ClientMsg.setForeground`)
+    /// so they know whether to defer to the phone's own Live Activity creation (foreground) or
+    /// push-to-start the glance themselves (backgrounded — the phone can't reliably start one). Starts
+    /// `true`: `onAppear` runs in the foreground; the background adopt-wake flips it first (§5.3).
+    private var isForeground = true
+    /// Host ids already told the *current* `isForeground` value — cleared whenever it flips so the
+    /// next sync re-notifies every host (mirrors `pushToStartSentTo`).
+    private var foregroundSentTo: Set<String> = []
 
     /// Guards `setupLiveActivityBridge` — it's called from both `onAppear` and the background adopt
     /// wake, and installing the callbacks / observers once is enough.