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;
     }
 }

Services/Audio/AudioSyncDelay.cs

@@ -0,0 +1,83 @@
+using System;
+
+namespace ytLive.Services.Audio;
+
+/// <summary>
+/// TASK 22: a fixed end-to-end audio delay applied to the interleaved stereo
+/// mix in <see cref="AudioMixer"/>. This is OBS's documented fix for the
+/// "audio is ahead of video" lip-sync case: delay the audio by a few
+/// milliseconds so it lands on the video. It is a pure delay line — input in,
+/// the same audio N ms later out — so it is trivially testable and carries no
+/// state outside its own ring.
+///
+/// Positive offsets only (0..500 ms). Advancing audio (<see cref="TimeSpan"/>
+/// would need a video-side delay and is out of scope for the audio layer.
+/// Changing the delay flushes the line, so a live slider change clicks rather
+/// than smearing. Safe to call from any thread — the mixer owns it.
+/// </summary>
+public sealed class AudioSyncDelay
+{
+    private readonly int _sampleRate;
+
+    private float[] _buffer = Array.Empty<float>();
+    private int _delaySamples;
+    private int _writePos;
+
+    public AudioSyncDelay(int sampleRate)
+    {
+        _sampleRate = Math.Max(1, sampleRate);
+        Configure(0);
+    }
+
+    /// <summary>Sets the delay in whole milliseconds (clamped to 0..500 and
+    /// flushed).</summary>
+    public void Configure(int delayMs)
+    {
+        _delaySamples = Frames(delayMs);
+        _buffer = new float[(_delaySamples + _sampleRate) * 2 + 1024];
+        _writePos = 0;
+    }
+
+    /// <summary>Delays an interleaved stereo chunk by the configured offset.
+    /// The returned length equals <paramref name="input"/>'s; the head is
+    /// silence until the line fills.</summary>
+    public void Process(ReadOnlySpan<float> input, Span<float> output)
+    {
+        if (output.Length < input.Length)
+            throw new ArgumentException("output must be at least as long as input", nameof(output));
+
+        var len = input.Length;
+        if (_delaySamples == 0)
+        {
+            input.CopyTo(output);
+            return;
+        }
+
+        var line = _buffer;
+        var lineLen = line.Length;
+        for (var i = 0; i < len; i++)
+        {
+            line[_writePos] = input[i];
+            _writePos++;
+            if (_writePos == lineLen)
+                _writePos = 0;
+        }
+
+        var readStart = (_writePos - _delaySamples - len + lineLen * 2) % lineLen;
+        for (var i = 0; i < len; i++)
+        {
+            var idx = readStart + i;
+            if (idx >= lineLen)
+                idx -= lineLen;
+            output[i] = line[idx];
+        }
+    }
+
+    private int Frames(int delayMs)
+    {
+        var clamped = Math.Clamp(delayMs, 0, 500);
+        // Interleaved stereo: each frame is two samples (L, R), so the delay
+        // in buffer positions is twice the frame count.
+        return (int)Math.Round(_sampleRate / 1000.0 * clamped) * 2;
+    }
+}

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()