perf(desktop): coalesce wake.feed frames

Sending one 80 ms frame per RPC is ~12.5 gateway calls/s for as long as the
ear is armed. Drain up to 4 queued frames into a single wake.feed payload
(backend feed() already splits long buffers into engine frames) — ~3 RPCs/s
steady-state. Fix the wake.feed size-cap comment (64000 bytes = 2 s, not
0.5 s).

apps/desktop/src/lib/wake-client-capture.ts

@@ -113,6 +113,9 @@ export async function startClientWakeCapture(
   // frames so the detector still sees contiguous recent PCM rather than gaps
   // from fire-and-forget discard-while-inflight.
   const MAX_QUEUED_FRAMES = 24 // ~1.9s at 80 ms/frame
+  // Coalesce queued frames into one wake.feed call (backend splits them back
+  // into engine frames). 4 × 80 ms ≈ 3 RPCs/s steady-state instead of 12.5.
+  const MAX_FRAMES_PER_FEED = 4
   const queue: Float32Array[] = []
   let draining = false
 
@@ -123,12 +126,14 @@ export async function startClientWakeCapture(
     draining = true
     try {
       while (!stopped && queue.length > 0) {
-        const frame = queue.shift()
-        if (!frame) {
+        const batch = queue.splice(0, MAX_FRAMES_PER_FEED)
+        if (batch.length === 0) {
           break
         }
         try {
-          const pcm = floatToInt16LE(frame)
+          const merged = new Float32Array(batch.length * frameLength)
+          batch.forEach((frame, i) => merged.set(frame, i * frameLength))
+          const pcm = floatToInt16LE(merged)
           await options.request('wake.feed', {
             pcm: bytesToBase64(pcm),
             sample_rate: TARGET_RATE

tui_gateway/server.py

@@ -13400,7 +13400,7 @@ def _(rid, params: dict) -> dict:
         return _err(rid, 4001, f"invalid base64 pcm: {e}")
     if not pcm:
         return _ok(rid, {"fed": False, "reason": "empty"})
-    # Soft size cap (~0.5s of 16kHz int16 mono = 16000 bytes)
+    # Soft size cap: 64000 bytes = 2s of 16 kHz int16 mono
     if len(pcm) > 64000:
         return _err(rid, 4001, "pcm frame too large")
     sr = params.get("sample_rate")