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/Audio/AudioMixer.cs

@@ -29,6 +29,8 @@ public sealed class AudioMixer : IDisposable
     private readonly Func<double>? _micGain;
     private readonly Func<double>? _loopbackGain;
     private readonly TimeSpan _mixInterval;
+    private readonly Func<int>? _syncOffsetMs;
+    private readonly AudioSyncDelay _syncDelay;
     private bool _started;
 
     // Live path (TASK 9): per-source resampling → voice chain on the mic →
@@ -45,6 +47,7 @@ public sealed class AudioMixer : IDisposable
     private float[]? _micChunk;
     private float[]? _loopbackChunk;
     private float[]? _mixBuffer;
+    private float[]? _delayedMix;
 
     public AudioMixer(
         IAudioSource mic,
@@ -52,6 +55,7 @@ public sealed class AudioMixer : IDisposable
         Action<string>? log = null,
         Func<double>? micGain = null,
         Func<double>? loopbackGain = null,
+        Func<int>? syncOffsetMs = null,
         TimeSpan? mixInterval = null)
     {
         _mic = mic;
@@ -61,6 +65,8 @@ public sealed class AudioMixer : IDisposable
         _log = log;
         _micGain = micGain;
         _loopbackGain = loopbackGain;
+        _syncOffsetMs = syncOffsetMs;
+        _syncDelay = new AudioSyncDelay(OutputSampleRate);
         _mixInterval = mixInterval ?? DefaultMixInterval;
 
         var seconds = _mixInterval.TotalSeconds;
@@ -333,6 +339,13 @@ public sealed class AudioMixer : IDisposable
             mix[i * 2 + 1] = m + loopbackChunk[i * 2 + 1] * loopGain;
         }
         _masterLimiter.Process(mix);
+
+        _syncDelay.Configure(_syncOffsetMs?.Invoke() ?? 0);
+        var delayed = _delayedMix!;
+        if (delayed.Length < mix.Length)
+            delayed = _delayedMix = new float[mix.Length];
+        _syncDelay.Process(mix, delayed);
+        Array.Copy(delayed, mix, mix.Length);
         return micRms;
     }
 }