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.

PROGRESS.md

@@ -42,9 +42,11 @@ cap the applied Opus hint at 30%, and feed it back over TLS.
 - Verify iOS remote-user tuning and private-conversation navigation with VoiceOver, including
   multiple streams, users without active streams, and users who disconnect while a view is open.
 - Exercise iOS background/lock, interruption, Bluetooth, route-change, ReplayKit, and iOS 27
-  ScreenCaptureKit paths on devices. Complete a 30-minute iOS call and Wi-Fi/cellular switching
-  with voice restoration, plus extended mono/stereo/voice-chat switching while joined. Verify
-  Windows desktop/per-app stereo sharing.
+  ScreenCaptureKit paths on devices. The background/lock gate keeps a call active for 15+ minutes
+  backgrounded and screen-locked with no periodic glitches and flat `VC_AUDIO` `feedDrops`/`starved`
+  counters (the render callback now paces the mix and the 20 ms capture handoff). Complete a
+  30-minute iOS call and Wi-Fi/cellular switching with voice restoration, plus extended
+  mono/stereo/voice-chat switching while joined. Verify Windows desktop/per-app stereo sharing.
 - Complete Developer ID signing/notarization. The iOS host and ReplayKit extension have been
   distribution-signed and packaged locally; upload the IPA for Apple's server-side validation.
 - Run the published Linux container and a 30-minute-or-longer server soak.