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/Models/FlowKeepAliveMode.swift

@@ -0,0 +1,39 @@
+// FlowKeepAliveMode.swift
+// OSGKeyboard · Shared
+//
+// User-selectable Flow session keep-alive strategy (mutually exclusive).
+
+import Foundation
+
+public enum FlowKeepAliveMode: String, CaseIterable, Identifiable, Sendable, Codable {
+    /// Continuous audio capture + Live Activity (current default behaviour).
+    case liveActivity = "liveActivity"
+    /// Picture-in-picture waveform keep-alive; mic released between utterances.
+    case pictureInPicture = "pictureInPicture"
+
+    public var id: String { rawValue }
+
+    /// Existing installs keep the Live Activity / continuous-capture path.
+    public static let `default`: FlowKeepAliveMode = .liveActivity
+
+    public var labelKey: String {
+        switch self {
+        case .liveActivity: return "settings.flow.keepAlive.liveActivity"
+        case .pictureInPicture: return "settings.flow.keepAlive.pictureInPicture"
+        }
+    }
+
+    public var subtitleKey: String {
+        switch self {
+        case .liveActivity: return "settings.flow.keepAlive.liveActivity.subtitle"
+        case .pictureInPicture: return "settings.flow.keepAlive.pictureInPicture.subtitle"
+        }
+    }
+
+    public static func fromStored(_ raw: String?) -> FlowKeepAliveMode {
+        guard let raw, let value = FlowKeepAliveMode(rawValue: raw) else {
+            return .default
+        }
+        return value
+    }
+}