chore(deps): Update dependencies and enhance API error handling

- Added '@vercel/analytics' to package.json for improved analytics tracking.
- Updated 'next' version from 15.0.2 to 15.0.3 to incorporate the latest features and fixes.
- Refactored API routes for invitations and studies to improve error handling and response structure.
- Enhanced permission checks in the invitations and studies API to ensure proper access control.
- Removed the participants dashboard page as part of a restructuring effort.
- Updated the database schema to include environment settings for users and studies.
- Improved the dashboard components to handle loading states and display statistics more effectively.

src/app/dashboard/page.tsx

@@ -72,7 +72,7 @@ export default function Dashboard() {
             <BookOpen className="h-4 w-4 text-muted-foreground" />
           </CardHeader>
           <CardContent>
-            <div className="text-2xl font-bold">{stats.studyCount}</div>
+            <div className="text-2xl font-bold">{stats.studyCount ? stats.studyCount : 0}</div>
             <p className="text-xs text-muted-foreground">Active research studies</p>
           </CardContent>
         </Card>