Fix TTS overlap deterministically, preserve message order, fix flaky Google login button

Overlay display duration is now computed server-side from estimated
reading time (text length / speaking rate), not from the audio
element's 'ended' event — edge-tts streams MP3 without a duration
header, and OBS's embedded browser fires 'ended' unreliably for that,
which is why the earlier event-based fix didn't hold up.

Per-streamer broadcasts are now serialized through a queue, so a
message waiting on an AI reply can no longer be overtaken by a later
message from a different viewer that doesn't need one.

Also fix the Google Sign-In button intermittently not rendering: the
GSI script tag is async/defer, and both index.html and send.html/js
called google.accounts.id.initialize() without waiting for it to
actually finish loading — a race that failed silently until the
script was cached from a previous load.

server.js

@@ -205,7 +205,20 @@ function synthesizeSpeech(text, voice) {
   });
 }
 
-function broadcastMessage(room, id, text, from, durationMs, ttsText, voice) {
+// edge-tts streams MP3 frames without a proper duration header (no Xing/VBRI
+// frame), which makes some players — including OBS's embedded CEF browser —
+// fire the audio element's 'ended' event unreliably (sometimes early). So we
+// don't trust that event for queue timing at all; instead we estimate how
+// long the text will take to read aloud and use that as the display floor,
+// which is deterministic regardless of the browser's audio-decoding quirks.
+function estimateSpeechMs(text) {
+  const CHARS_PER_SECOND = 15; // conservative reading speed for ru/en TTS voices
+  const STARTUP_BUFFER_MS = 800; // covers synthesis/playback startup latency
+  return STARTUP_BUFFER_MS + Math.ceil(text.length / CHARS_PER_SECOND) * 1000;
+}
+
+function broadcastMessage(room, id, text, from, minDurationMs, ttsText, voice) {
+  const durationMs = Math.max(minDurationMs, estimateSpeechMs(ttsText));
   io.to(room).emit('display_message', { id, text, from, at: Date.now(), durationMs });
 
   synthesizeSpeech(ttsText, voice)
@@ -256,6 +269,20 @@ async function getAiReply(text, aiName) {
   return data.choices[0].message.content.trim();
 }
 
+// Per-streamer chain of pending broadcasts. Without this, a message waiting
+// on an AI reply (a network round-trip, ~1-3s) could be overtaken by a later
+// message from a different viewer that doesn't need one — this makes
+// broadcast order match send order instead of "whichever finished first".
+const broadcastQueues = new Map();
+
+function enqueueBroadcast(streamerId, task) {
+  const previous = broadcastQueues.get(streamerId) || Promise.resolve();
+  const next = previous.then(task, task).catch((err) => {
+    console.error('[broadcast-queue] task failed:', err);
+  });
+  broadcastQueues.set(streamerId, next);
+}
+
 io.on('connection', (socket) => {
   const { role, token } = socket.handshake.query;
   const connectedUser = socket.request.session.user;
@@ -327,13 +354,17 @@ io.on('connection', (socket) => {
         );
       };
 
-      if (aiReply && DEEPSEEK_API_KEY) {
-        const aiName = streamer.ai_name || 'Альтушка Ирина';
-        // Wait for the AI reply text before showing anything, so the viewer's
-        // message and the AI reply land in the overlay queue back-to-back
-        // instead of the reply trailing in later with an awkward gap.
-        getAiReply(message, aiName)
-          .then((replyText) => {
+      // Broadcasting is enqueued per-streamer so it happens in send order —
+      // otherwise a message waiting on an AI reply could be overtaken by a
+      // later message from another viewer that doesn't need one.
+      enqueueBroadcast(streamer.id, async () => {
+        if (aiReply && DEEPSEEK_API_KEY) {
+          const aiName = streamer.ai_name || 'Альтушка Ирина';
+          // Wait for the AI reply text before showing anything, so the viewer's
+          // message and the AI reply land in the overlay queue back-to-back
+          // instead of the reply trailing in later with an awkward gap.
+          try {
+            const replyText = await getAiReply(message, aiName);
             broadcastOriginal();
 
             const aiMessageId = crypto.randomUUID();
@@ -343,14 +374,14 @@ io.on('connection', (socket) => {
               `${aiName} отвечает. ${replyText}`,
               AI_VOICE
             );
-          })
-          .catch((err) => {
+          } catch (err) {
             console.error('[ai] DeepSeek reply failed:', err);
             broadcastOriginal();
-          });
-      } else {
-        broadcastOriginal();
-      }
+          }
+        } else {
+          broadcastOriginal();
+        }
+      });
     });
   });
 });