feat: schedule automatic form closure

app/form/[id]/page.tsx

@@ -11,6 +11,7 @@ import {
   type FormAnswerValue,
 } from "@/lib/form-answer-values";
 import { getFormSubmissionStats } from "@/lib/form-submission-stats";
+import { isFormAcceptingSubmissions } from "@/lib/form-availability";
 
 export const dynamic = "force-dynamic";
 
@@ -98,7 +99,11 @@ export default async function FormsSubmitPage(
       <RealtimeRefresh topic="forms" formId={form.id} />
       <div className="mx-auto max-w-2xl">
         <FormFillerClient 
-          form={form} 
+          form={{
+            ...form,
+            isOpen: isFormAcceptingSubmissions(form),
+            closesAt: form.closesAt?.toISOString() ?? null,
+          }}
           questions={questionsList} 
           initialAnswers={initialAnswers} 
           hasSubmission={Boolean(existingSubmission)}