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/AppGroupConfigurationTests.swift

@@ -33,6 +33,7 @@ final class AppGroupConfigurationTests: XCTestCase {
         XCTAssertEqual(config.polishIntensity, .default)
         XCTAssertTrue(config.personalDictionary.entries.isEmpty)
         XCTAssertTrue(config.flowSkipAppSwitch)
+        XCTAssertEqual(config.flowKeepAliveMode, .liveActivity)
         XCTAssertEqual(config.flowInactivityDuration, .fiveMinutes)
     }
 
@@ -58,6 +59,7 @@ final class AppGroupConfigurationTests: XCTestCase {
         config.cursorDragNavigationEnabled = false
         config.polishIntensity = .light
         config.flowSkipAppSwitch = false
+        config.flowKeepAliveMode = .pictureInPicture
         // Use a non-default value so the round-trip actually proves persistence.
         config.flowInactivityDuration = .threeHours
         config.save(to: defaults)
@@ -81,6 +83,7 @@ final class AppGroupConfigurationTests: XCTestCase {
         XCTAssertFalse(loaded.cursorDragNavigationEnabled)
         XCTAssertEqual(loaded.polishIntensity, .light)
         XCTAssertFalse(loaded.flowSkipAppSwitch)
+        XCTAssertEqual(loaded.flowKeepAliveMode, .pictureInPicture)
         XCTAssertEqual(loaded.flowInactivityDuration, .threeHours)
     }
 

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)

OSGKeyboardTests/SettingsCloudSyncTests.swift

@@ -62,6 +62,7 @@ final class SettingsCloudSyncTests: XCTestCase {
             polishIntensity: SyncedField(value: .medium, updatedAt: stampA, deviceID: deviceA),
             llmThinkingEnabled: SyncedField(value: false, updatedAt: stampA, deviceID: deviceA),
             flowSkipAppSwitch: SyncedField(value: true, updatedAt: stampA, deviceID: deviceA),
+            flowKeepAliveMode: SyncedField(value: .liveActivity, updatedAt: stampA, deviceID: deviceA),
             flowInactivityDuration: SyncedField(value: .twelveHours, updatedAt: stampA, deviceID: deviceA)
         )
         let remote = SyncedAppSettingsV2(
@@ -82,6 +83,7 @@ final class SettingsCloudSyncTests: XCTestCase {
             polishIntensity: SyncedField(value: .light, updatedAt: stampB, deviceID: deviceB),
             llmThinkingEnabled: SyncedField(value: true, updatedAt: stampB, deviceID: deviceB),
             flowSkipAppSwitch: SyncedField(value: false, updatedAt: stampB, deviceID: deviceB),
+            flowKeepAliveMode: SyncedField(value: .pictureInPicture, updatedAt: stampB, deviceID: deviceB),
             flowInactivityDuration: SyncedField(value: .threeHours, updatedAt: stampB, deviceID: deviceB)
         )