Fix rounds management bugs and invitation flow

- Fix rounds list showing 0 projects by adding _count to program.list query
- Fix round reordering by using correct cache invalidation params
- Fix finalizeResults to auto-advance passed projects to next round
- Fix member list not updating after add/remove by invalidating user.list
- Fix invitation link error page by correcting path from /auth-error to /error
- Add /apply, /verify, /error to public paths in auth config

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/lib/auth.config.ts

@@ -39,9 +39,11 @@ export const authConfig: NextAuthConfig = {
       // Public paths that don't require authentication
       const publicPaths = [
         '/login',
+        '/verify',
         '/verify-email',
-        '/auth-error',
+        '/error',
         '/accept-invite',
+        '/apply',
         '/api/auth',
       ]
 
@@ -78,7 +80,7 @@ export const authConfig: NextAuthConfig = {
   pages: {
     signIn: '/login',
     verifyRequest: '/verify-email',
-    error: '/auth-error',
+    error: '/error',
     newUser: '/set-password',
   },
   session: {