Let streamers name their AI assistant; fix overlay TTS audio overlap

Streamer dashboard gains an editable AI assistant name (default
"Альтушка Ирина"), stored per-streamer and used for the overlay label,
TTS intro, and DeepSeek system prompt. Also fixes a bug where a long
message's TTS audio could still be playing when the next queued
message started its own audio — the overlay queue now waits for the
current audio to actually finish (not just the configured display
duration) before advancing.

public/overlay.js

@@ -45,9 +45,15 @@ function playNotificationSound() {
   }
 }
 
-function playSpeech(base64Audio, mimeType) {
+function playSpeech(base64Audio, mimeType, onEnded) {
   const audio = new Audio(`data:${mimeType};base64,${base64Audio}`);
-  audio.play().catch((err) => console.error('Could not play TTS audio:', err));
+  const done = () => { if (onEnded) onEnded(); };
+  audio.addEventListener('ended', done);
+  audio.addEventListener('error', done);
+  audio.play().catch((err) => {
+    console.error('Could not play TTS audio:', err);
+    done();
+  });
 }
 
 function advanceQueue() {
@@ -62,14 +68,37 @@ function advanceQueue() {
   box.classList.add('visible');
 
   playNotificationSound();
-  if (current.audio) {
-    playSpeech(current.audio.data, current.audio.mimeType);
-  }
 
-  setTimeout(() => {
+  // The message stays up for at least durationMs (streamer's configured
+  // display time), but if its TTS audio is still playing when that timer
+  // fires (e.g. a long question read aloud), we must not start the next
+  // message's audio on top of it — so we also wait for the audio to
+  // actually finish before advancing.
+  let minTimeElapsed = false;
+  let audioFinished = !current.audio;
+
+  const maybeAdvance = () => {
+    if (!minTimeElapsed || !audioFinished) return;
     box.classList.remove('visible');
     current = null;
     setTimeout(advanceQueue, FADE_MS);
+  };
+
+  current.startAudio = (audio) => {
+    audioFinished = false;
+    playSpeech(audio.data, audio.mimeType, () => {
+      audioFinished = true;
+      maybeAdvance();
+    });
+  };
+
+  if (current.audio) {
+    current.startAudio(current.audio);
+  }
+
+  setTimeout(() => {
+    minTimeElapsed = true;
+    maybeAdvance();
   }, current.durationMs || 10000);
 }
 
@@ -87,7 +116,7 @@ socket.on('display_message', (payload) => {
 socket.on('display_audio', (payload) => {
   const audio = { data: payload.audio, mimeType: payload.mimeType };
   if (current && current.id === payload.id) {
-    playSpeech(audio.data, audio.mimeType);
+    current.startAudio(audio);
     return;
   }
   const queued = queue.find((item) => item.id === payload.id);