TASK 22: global audio sync offset (positive delay at the mixer out)

Adds AudioSyncOffsetMs (0..500ms, default 0) that delays the whole
interleaved-stereo mix so audio lands on the video when it runs ahead —
OBS's documented lip-sync fix. Positive-only: advancing audio needs a
video-side delay and is out of the audio layer's scope.

- Services/Audio/AudioSyncDelay.cs: pure delay line, flushed on Configure
- AudioMixer: Func<int> syncOffsetMs seam + delay applied post-limiter
- LayoutStore.Settings + MainViewModel.Audio/VM: load/save + binding
- PreviewPane mic bar: SYNC slider + status dot (IntToSyncBrushConverter)
- AudioSyncDelayTests: identity, negative/beyond-500 clamps, 10ms→960 samples

Reference (external scan): https://obs-versions.com/blog/how-to-fix-audio-delay-on-obs
(audio ahead => positive delay). Verified: build 0 warnings; 3/3 delay tests pass.

ai.md

@@ -155,7 +155,7 @@ C# / WPF (.NET 8) following MVVM:
 |------|------|
 | `Models/` | Plain data types — Scene, Source (incl. `ClipShape`, `IsMirrored`, `VideoImageSource`), QualityOption, StreamConfig, StreamHealth, YouTubeChannel, ChatMessage, **Socials (`SocialService` enum + `SocialEntry`/`SocialsConfig` + `SocialServiceIcons`) — the social bar** |
 | `ViewModels/` | MainViewModel — `public partial class`, one file per functional area (Scenes, Background, Webcam, Audio, Trax, Socials, Streaming, Chat, Overlays, Account, License, Recording — split complete, see `ViewModels/index.md`); **Chat.cs is a thin delegating facade over `Services/ChatOverlayLayer.cs` (Commit G, first true decomposition)**; GoLiveViewModel, ReuseImageViewModel, CameraPickerViewModel, **SocialsDialogViewModel** |
-| `Services/` | YouTube OAuth2, stream/broadcast management, live chat polling, LayoutStore (SQLite), **SocialValidator (`ISocialValidator` seam + `HttpSocialValidator` default)**, **webcam: `VideoFrame` seam + `CameraDeviceInfo`/`ICameraEnumerator`/`ICameraFrameSource` interfaces + `MediaCaptureCameraEnumerator`/`MediaCaptureFrameSource` (WinRT) + `CameraManager`**, **screen capture: `IFullScreenDetector`/`Win32FullScreenDetector` + `IScreenCaptureSource`/`ScreenCaptureFrameSource` (WinRT GraphicsCapture) + `ScreenCaptureManager` + `ScreenCaptureSourceFactory` + `Direct3D11Helper`/`CaptureInterop` (COM bridges)**, **compositor: `SceneCompositor` + `CompositorOptions` + pure `StretchMath` + `StaticPixelCache` (see "Scene compositor")**, **audio: `IAudioSource` seam + `WasapiLoopbackAudioSource`/`WasapiMicAudioSource` (NAudio WASAPI) + `AudioMixer` + pure `AudioLevelMeter`/`WaveToFloat`/`VoiceFilterChain`/`LowShelfFilter`/`HighShelfFilter`/`NoiseGate`/`Compressor`/`AutoDucker`/`AudioRingBuffer`/`TinyResampler` + `MusicPlayer` + `IAudioPipeWriter`/`NamedPipeAudioWriter` (see "Live audio capture")**, **encoder: `IFfmpegEncoder`/`FfmpegEncoder` + `IEncoderProcess`/`FfmpegEncoderProcess` + `IFfmpegLocator`/`FfmpegLocator` + pure `FfmpegArgs`/`FfmpegProgressParser`/`FfmpegEncoderPicker` + the `FramePump` frame producer (see "Live encoder" + "Live frame pipeline")**, **notifications: `INotificationService` seam (`AppNotificationSeverity` Info/Success/Warning/Error) + `NotificationService` (Notification.Wpf toasts, see "Toast notifications")** |
+| `Services/` | YouTube OAuth2, stream/broadcast management, live chat polling, LayoutStore (SQLite), **SocialValidator (`ISocialValidator` seam + `HttpSocialValidator` default)**, **webcam: `VideoFrame` seam + `CameraDeviceInfo`/`ICameraEnumerator`/`ICameraFrameSource` interfaces + `MediaCaptureCameraEnumerator`/`MediaCaptureFrameSource` (WinRT) + `CameraManager`**, **screen capture: `IFullScreenDetector`/`Win32FullScreenDetector` + `IScreenCaptureSource`/`ScreenCaptureFrameSource` (WinRT GraphicsCapture) + `ScreenCaptureManager` + `ScreenCaptureSourceFactory` + `Direct3D11Helper`/`CaptureInterop` (COM bridges)**, **compositor: `SceneCompositor` + `CompositorOptions` + pure `StretchMath` + `StaticPixelCache` (see "Scene compositor")**, **audio: `IAudioSource` seam + `WasapiLoopbackAudioSource`/`WasapiMicAudioSource` (NAudio WASAPI) + `AudioMixer` + pure `AudioLevelMeter`/`WaveToFloat`/`VoiceFilterChain`/`LowShelfFilter`/`HighShelfFilter`/`NoiseGate`/`Compressor`/`AutoDucker`/`AudioRingBuffer`/`TinyResampler`/`AudioSyncDelay` + `MusicPlayer` + `IAudioPipeWriter`/`NamedPipeAudioWriter` (see "Live audio capture")**, **encoder: `IFfmpegEncoder`/`FfmpegEncoder` + `IEncoderProcess`/`FfmpegEncoderProcess` + `IFfmpegLocator`/`FfmpegLocator` + pure `FfmpegArgs`/`FfmpegProgressParser`/`FfmpegEncoderPicker` + the `FramePump` frame producer (see "Live encoder" + "Live frame pipeline")**, **notifications: `INotificationService` seam (`AppNotificationSeverity` Info/Success/Warning/Error) + `NotificationService` (Notification.Wpf toasts, see "Toast notifications")** |
 | `Helpers/` | ViewModelBase (INotifyPropertyChanged), RelayCommand, ImageCache, AppLog (file logger), FocusPreservingListBox, OAuthCredentials, **TokenStore (DPAPI session persistence)**, visibility converters |
 | `Themes/` | `Controls.xaml` — the single dark-theme source, merged once in `App.xaml` (see `Themes/index.md`) |
 | `MainWindow.xaml` | Dark theme; layout: top bar (controls), center (preview + live controls below), left (scenes/sources), right (chat), bottom (gear + stream stats + resolution) |
@@ -589,6 +589,13 @@ devices, no timers).
   `StopLive()` (closes the pipe → ffmpeg audio EOF) **BEFORE** stopping the frame pump (video EOF) —
   the reverse order stalls on pipe backpressure. `FfmpegEncoder` itself is untouched; the VM owns the
   pipe lifecycle.
+- **Audio sync offset (TASK 22):** after the limiter, `FillAndMix` routes the whole interleaved stereo
+  mix through a **`AudioSyncDelay`** (`Services/Audio/AudioSyncDelay.cs`) — a pure delay line whose
+  offset comes from a `Func<int> syncOffsetMs` seam (the VM's global `AudioSyncOffsetMs`, 0..500 ms,
+  persisted as `Audio.SyncOffsetMs`). This is OBS's documented fix for audio running ahead of the video
+  (delay it a few ms); positive-only, since advancing audio would need a video-side delay. A slider on
+  the mic bar + a status dot (`IntToSyncBrushConverter`) surface it. Changing the delay flushes the line
+  (a live change clicks rather than smears).
 - **TRAX — free background music (TASK 8):** `MusicPlayer` = NAudio `MediaFoundationReader`
   (mp3/wav/m4a) → `VolumeWaveProvider16` at the hardcoded **0.20** bed (no slider) → `WaveOutEvent` on
   the default device, **looping on any clean natural end** (`PlaybackStopped` with `e.Exception == null`