feat(webui): remember-me checkbox on the login page

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/app/login/page.tsx

@@ -16,6 +16,7 @@ export default function LoginPage() {
   const [username, setUsername] = useState("");
   const [password, setPassword] = useState("");
   const [error, setError] = useState<string | null>(null);
+  const [rememberMe, setRememberMe] = useState(false);
   const [submitting, setSubmitting] = useState(false);
 
   const submit = async (event: FormEvent<HTMLFormElement>) => {
@@ -28,7 +29,7 @@ export default function LoginPage() {
         method: "POST",
         headers: { "Content-Type": "application/json" },
         credentials: "same-origin",
-        body: JSON.stringify({ username, password, next: returnPath() }),
+        body: JSON.stringify({ username, password, next: returnPath(), rememberMe }),
       });
       const body = (await response.json().catch(() => ({}))) as {
         error?: string;
@@ -87,6 +88,17 @@ export default function LoginPage() {
               required
             />
           </label>
+          <label className="flex items-center gap-2 text-sm text-muted-foreground">
+            <input
+              type="checkbox"
+              name="rememberMe"
+              checked={rememberMe}
+              onChange={(event) => setRememberMe(event.target.checked)}
+              disabled={submitting}
+              className="h-4 w-4"
+            />
+            <span>Remember me for 30 days</span>
+          </label>
         </div>
         {error && (
           <p className="mt-4 text-sm text-destructive" role="alert">