Implement UUID-based tracking for OBS groups to handle renames

- Add group_uuid column to teams table for reliable OBS scene tracking
- Update createGroup API to store OBS scene UUID when creating groups
- Enhance verifyGroups API with UUID-first matching and name fallback
- Add comprehensive verification system to detect sync issues between database and OBS
- Implement UI indicators for UUID linking, name mismatches, and invalid groups
- Add "Clear Invalid" and "Update Name" actions for fixing synchronization problems
- Create migration script for existing databases to add UUID column
- Update Team type definition to include optional group_uuid field

This resolves issues where manually renaming groups in OBS would break the synchronization
between the database and OBS, providing a more robust group management system.

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

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

app/api/createGroup/route.ts

@@ -43,15 +43,15 @@ export async function POST(request: NextRequest) {
       suffix: 'sat'
     });
 
-    // Update team with group name
-    await db.run(
-      `UPDATE ${teamsTableName} SET group_name = ? WHERE team_id = ?`,
-      [sanitizedGroupName, validTeamId]
-    );
-
-    // Create group in OBS
+    // Create group in OBS first to get UUID
     const result = await createGroupIfNotExists(sanitizedGroupName);
 
+    // Update team with group name and UUID
+    await db.run(
+      `UPDATE ${teamsTableName} SET group_name = ?, group_uuid = ? WHERE team_id = ?`,
+      [sanitizedGroupName, result.sceneUuid, validTeamId]
+    );
+
     await db.close();
 
     return NextResponse.json({