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.

Services/LayoutStore.Settings.cs

@@ -29,6 +29,19 @@ public partial class LayoutStore : IDisposable
         insert.ExecuteNonQuery();
     }
 
+    /// <summary>The global audio-sync delay in milliseconds (TASK 22), 0..500,
+    /// default 0. Restored at startup so the mixer starts on the user's offset.</summary>
+    public int LoadAudioSyncOffsetMs()
+    {
+        var value = GetSetting("Audio.SyncOffsetMs");
+        return int.TryParse(value, out var ms) ? Math.Clamp(ms, 0, 500) : 0;
+    }
+
+    public void SaveAudioSyncOffsetMs(int ms)
+    {
+        UpsertSetting("Audio.SyncOffsetMs", Math.Clamp(ms, 0, 500).ToString());
+    }
+
     /// <summary>The user's chosen record output folder (TASK 18), or null to use the
     /// default <c>%APPDATA%\ytLlive\recordings</c>. Restored at startup.</summary>
     public string? LoadRecordFolder()