feat: add player count to stacked room info

Adds player count as third line in the combined mode/room pill:

**3-line vertical stack:**
1. Mode indicator: ⚔️ Battle (12px, bold, mode color)
2. Room name: Auto-generated Room (11px, semibold, light purple)
3. Player count: 2 players (9px, medium, lighter purple)

Styling:
- Player count uses smaller text (9px vs 11px)
- Lighter opacity (0.6 vs 0.8) for visual hierarchy
- Proper singular/plural handling
- lineHeight: 1 for tight spacing

Result: Compact info pill with all relevant room details in one place,
properly hierarchical with decreasing emphasis from mode → name → count.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

apps/web/src/components/nav/RoomInfo.tsx

@@ -81,7 +81,7 @@ export function RoomInfo({
               <span style={{ lineHeight: 1 }}>{modeLabel}</span>
             </div>
 
-            {/* Bottom: Room name */}
+            {/* Middle: Room name */}
             <div
               style={{
                 fontSize: '11px',
@@ -92,6 +92,18 @@ export function RoomInfo({
             >
               {displayName}
             </div>
+
+            {/* Bottom: Player count */}
+            <div
+              style={{
+                fontSize: '9px',
+                fontWeight: '500',
+                color: 'rgba(196, 181, 253, 0.6)',
+                lineHeight: 1,
+              }}
+            >
+              {playerCount} {playerCount === 1 ? 'player' : 'players'}
+            </div>
           </div>
         </Tooltip.Trigger>