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/components/admin/user-actions.tsx

@@ -2,7 +2,6 @@
 
 import { useState } from 'react'
 import Link from 'next/link'
-import { useRouter } from 'next/navigation'
 import { trpc } from '@/lib/trpc/client'
 import { Button } from '@/components/ui/button'
 import {
@@ -38,12 +37,17 @@ interface UserActionsProps {
 }
 
 export function UserActions({ userId, userEmail, userStatus }: UserActionsProps) {
-  const router = useRouter()
   const [showDeleteDialog, setShowDeleteDialog] = useState(false)
   const [isSending, setIsSending] = useState(false)
 
+  const utils = trpc.useUtils()
   const sendInvitation = trpc.user.sendInvitation.useMutation()
-  const deleteUser = trpc.user.delete.useMutation()
+  const deleteUser = trpc.user.delete.useMutation({
+    onSuccess: () => {
+      // Invalidate user list to refresh the members table
+      utils.user.list.invalidate()
+    },
+  })
 
   const handleSendInvitation = async () => {
     if (userStatus !== 'INVITED') {
@@ -55,6 +59,8 @@ export function UserActions({ userId, userEmail, userStatus }: UserActionsProps)
     try {
       await sendInvitation.mutateAsync({ userId })
       toast.success(`Invitation sent to ${userEmail}`)
+      // Invalidate in case status changed
+      utils.user.list.invalidate()
     } catch (error) {
       toast.error(error instanceof Error ? error.message : 'Failed to send invitation')
     } finally {
@@ -67,7 +73,6 @@ export function UserActions({ userId, userEmail, userStatus }: UserActionsProps)
       await deleteUser.mutateAsync({ id: userId })
       toast.success('User deleted successfully')
       setShowDeleteDialog(false)
-      router.refresh()
     } catch (error) {
       toast.error(error instanceof Error ? error.message : 'Failed to delete user')
     }