Fix iOS background audio pacing

Sleep-paced threads stall for hundreds of milliseconds when iOS coalesces a
backgrounded app's wakeups, and the deadline resets that discarded the deficit
left the capture backlog queued until its ring overflowed: regular dropouts
that worsen the longer the app stays backgrounded. Pace both 20 ms hands-offs
from the AVAudioSourceNode render callback instead (mix via Audio.RunCycle
with deviceClockedAudio, capture handoff from the ring), wake the UDP sender
on a queue signal instead of a 1 ms poll, and let stalled consumers drop their
backlog to the buffer target instead of ratcheting it.

tests/VoiceCat.Tests/PublishServerScriptTests.cs

@@ -132,6 +132,16 @@ public class PublishServerScriptTests
         Assert.DoesNotContain("Task.Delay(10", screen);
         Assert.Contains("MaximumCaptureCallbackFrames = 16_384", microphone);
         Assert.DoesNotContain("Math.Ceiling(4_096 * 48_000", microphone);
+
+        // Both 20 ms hands-offs run from the AVAudioSourceNode render callback: sleep-paced
+        // threads coalesce when the app is backgrounded and glitch the call after several minutes.
+        string model = await File.ReadAllTextAsync(Path.Combine(
+            root, "clients", "apple", "VoiceCat.iOS", "AppModel.cs"));
+        Assert.DoesNotContain("new Thread(", microphone);
+        Assert.DoesNotContain("Thread.Sleep", microphone);
+        Assert.Contains("owner.Audio.RunCycle()", microphone);
+        Assert.Contains("while (microphoneCredit >= 960)", microphone);
+        Assert.Contains("deviceClockedAudio: true", model);
     }
 
     [Fact]