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/send.js

@@ -6,6 +6,7 @@ const logoutBtn = document.getElementById('logout');
 const displayNameInput = document.getElementById('display-name');
 const messageInput = document.getElementById('message');
 const aiReplyCheckbox = document.getElementById('ai-reply');
+const aiReplyLabel = document.getElementById('ai-reply-label');
 const sendBtn = document.getElementById('send');
 const statusEl = document.getElementById('status');
 
@@ -51,7 +52,16 @@ async function handleCredentialResponse(response) {
   }
 }
 
+async function loadAiName() {
+  const res = await fetch(`/api/streamer-info?token=${encodeURIComponent(token)}`);
+  if (!res.ok) return;
+  const { aiName } = await res.json();
+  if (aiName) aiReplyLabel.textContent = `Задать вопрос: ${aiName} 🤖`;
+}
+
 async function init() {
+  loadAiName();
+
   const configRes = await fetch('/config');
   const { googleClientId } = await configRes.json();