Invalidate the router on sign out so account orders clear immediately

Signing out only clears the auth session cookie; a route already
loaded (e.g. /orders) keeps its stale loader data until something
triggers a reload. Call router.invalidate() once signOut succeeds so
the current route's loader reruns against the now-signed-out session.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/integrations/better-auth/header-user.tsx

@@ -1,4 +1,4 @@
-import { Link, useRouterState } from '@tanstack/react-router'
+import { Link, useRouter, useRouterState } from '@tanstack/react-router'
 import { useEffect, useRef, useState } from 'react'
 
 import { authClient } from '#/lib/auth-client'
@@ -66,6 +66,7 @@ const LogOutIcon = () => (
 const BetterAuthHeader = () => {
   const { data: session, isPending } = authClient.useSession()
   const { clear: clearBasket } = useBasket()
+  const router = useRouter()
   const [open, setOpen] = useState(false)
   const wrapperRef = useRef<HTMLDivElement>(null)
   const pathname = useRouterState({
@@ -150,7 +151,11 @@ const BetterAuthHeader = () => {
                   setOpen(false)
                   clearGuestOrderRefs()
                   clearBasket()
-                  void authClient.signOut()
+                  void authClient.signOut({
+                    fetchOptions: {
+                      onSuccess: () => void router.invalidate(),
+                    },
+                  })
                 }}
               >
                 <LogOutIcon />