feat(flow): add Picture in Picture keep-alive mode

- Add FlowKeepAliveMode (Dynamic Island vs PiP) with iCloud sync
- Settings: keep-alive picker; inactivity timeout only for Live Activity
- PiP: waveform sample-buffer controller, mic released between utterances
- PiP sessions have no idle expiry; user closing PiP ends the session
- FlowSessionManager branches hostReady, session start, and utterance paths
- UIBackgroundModes picture-in-picture; bilingual strings and tests

Co-authored-by: Rocky <hkgood@users.noreply.github.com>

OSGKeyboardShared/Services/FlowSessionPolicy.swift

@@ -25,6 +25,18 @@ public enum FlowSessionPolicy {
         inactivityDuration(defaults: defaults).timeInterval
     }
 
+    public static func keepAliveMode(defaults: UserDefaults? = nil) -> FlowKeepAliveMode {
+        let store = resolvedDefaults(defaults)
+        return FlowKeepAliveMode.fromStored(
+            store.string(forKey: AppGroupConfiguration.Keys.flowKeepAliveMode)
+        )
+    }
+
+    /// PiP sessions have no inactivity expiry; only the Live Activity path times out.
+    public static func usesInactivityExpiry(defaults: UserDefaults? = nil) -> Bool {
+        keepAliveMode(defaults: defaults) == .liveActivity
+    }
+
     private static func resolvedDefaults(_ defaults: UserDefaults?) -> UserDefaults {
         if let defaults { return defaults }
         guard let available = AppGroup.defaultsIfAvailable else {