Add Conferences and audio-only Rooms, plus mobile schedule icon.

Split town_hall into a Conferences sidebar flow and Spaces-style Rooms with host/speaker/listener roles; enforce audio-only LiveKit UI for rooms; show schedule icon on mobile meetings index.

Co-authored-by: Cursor <cursoragent@cursor.com>

app/Models/Room.php

@@ -81,6 +81,21 @@ class Room extends Model
         return $this->type === 'webinar';
     }
 
+    public function isConference(): bool
+    {
+        return $this->type === 'town_hall';
+    }
+
+    public function isSpace(): bool
+    {
+        return $this->type === 'space';
+    }
+
+    public function isAudioOnly(): bool
+    {
+        return $this->isSpace() || (bool) $this->setting('audio_only', false);
+    }
+
     public function canRestart(): bool
     {
         if ($this->status === 'cancelled' || $this->activeSession()) {
@@ -100,6 +115,14 @@ class Room extends Model
             return $restarting ? 'Restart webinar' : 'Start webinar';
         }
 
+        if ($this->isConference()) {
+            return $restarting ? 'Restart conference' : 'Start conference';
+        }
+
+        if ($this->isSpace()) {
+            return $restarting ? 'Reopen room' : 'Open room';
+        }
+
         return $restarting ? 'Restart meeting' : 'Start meeting';
     }