feat(extension): send nothing to the server while alone in a room

When no other peer is present, heartbeats, force-sync, and episode auto-sync
are now fully suppressed (previously the keepAlive heartbeat, force-sync, and
episode lobby were still broadcast to an empty room):
- keepAlive heartbeat gated on a live peer count
- force-sync is a no-op when solo (no pause-then-timeout freeze, no traffic)
- episode auto-sync skips the lobby entirely and just plays the next episode

The solo state is recomputed live from the current peer list on every event
(never cached), so the instant another peer joins syncing resumes. On that
solo->not-solo transition the background also requests an immediate heartbeat
from the content script so the newcomer sees the current position without
waiting for the next interval.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

extension/content.js

@@ -538,6 +538,14 @@
             return true;
         }
 
+        // Background asks for an immediate state push (e.g. the first peer just
+        // joined while we were solo) so the newcomer syncs without waiting.
+        if (message.type === 'REQUEST_HEARTBEAT') {
+            sendHeartbeat();
+            sendResponse({ ok: true });
+            return true;
+        }
+
         if (message.type === 'SERVER_COMMAND') {
             const { action, payload } = message;
             let actionCompleted = false;