Fix dropdown optimistic updates to use correct stream group names

- Include team name prefix in optimistic update stream group generation
- Format: {team_name}_{stream_name}_stream to match backend file writes
- Prevents dropdown from reverting to wrong value after selection
- Now dropdown shows correct selection immediately without requiring page refresh

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

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

app/page.tsx

@@ -93,9 +93,9 @@ export default function Home() {
   const handleSetActive = useCallback(async (screen: ScreenType, id: number | null) => {
     const selectedStream = streams.find((stream) => stream.id === id);
 
-    // Generate stream group name for optimistic updates
+    // Generate stream group name for optimistic updates - must match obsClient.js format
     const streamGroupName = selectedStream 
-      ? `${selectedStream.name.toLowerCase().replace(/\s+/g, '_')}_stream`
+      ? `${selectedStream.team_name?.toLowerCase().replace(/\s+/g, '_') || 'unknown'}_${selectedStream.name.toLowerCase().replace(/\s+/g, '_')}_stream`
       : null;
 
     // Update local state immediately for optimistic updates