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/app/(admin)/admin/members/invite/page.tsx

@@ -117,7 +117,13 @@ export default function MemberInvitePage() {
     skipped: number
   } | null>(null)
 
-  const bulkCreate = trpc.user.bulkCreate.useMutation()
+  const utils = trpc.useUtils()
+  const bulkCreate = trpc.user.bulkCreate.useMutation({
+    onSuccess: () => {
+      // Invalidate user list to refresh the members table when navigating back
+      utils.user.list.invalidate()
+    },
+  })
 
   // --- Manual entry helpers ---
   const updateRow = (id: string, field: keyof MemberRow, value: string | string[]) => {