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>

OSGKeyboardTests/FlowSessionPolicyTests.swift

@@ -29,6 +29,25 @@ final class FlowSessionPolicyTests: XCTestCase {
         XCTAssertEqual(FlowInactivityDuration.tenMinutes.timeInterval, 10 * 60)
     }
 
+    func testKeepAliveModeDefaultsToLiveActivity() {
+        let defaults = makeDefaults()
+        XCTAssertEqual(FlowSessionPolicy.keepAliveMode(defaults: defaults), .liveActivity)
+        XCTAssertTrue(FlowSessionPolicy.usesInactivityExpiry(defaults: defaults))
+    }
+
+    func testPiPSessionHasNoInactivityExpiry() {
+        let defaults = makeDefaults()
+        defaults.set(FlowKeepAliveMode.pictureInPicture.rawValue,
+                     forKey: AppGroupConfiguration.Keys.flowKeepAliveMode)
+        FlowSessionBridge.markSessionActive(sessionId: UUID(), defaults: defaults)
+
+        XCTAssertTrue(FlowSessionBridge.isSessionActive(defaults: defaults))
+        XCTAssertNil(FlowSessionBridge.sessionExpiresAt(defaults: defaults))
+
+        FlowSessionBridge.touchLastActivity(defaults: defaults)
+        XCTAssertNil(FlowSessionBridge.sessionExpiresAt(defaults: defaults))
+    }
+
     func testTouchLastActivityExtendsExpiry() {
         let defaults = makeDefaults()
         defaults.set(FlowInactivityDuration.tenMinutes.rawValue, forKey: AppGroupConfiguration.Keys.flowInactivityDuration)