to set a cookie does not work

import type { BetterAuthPlugin } from 'better-auth';
import { createAuthEndpoint } from 'better-auth/api';
import { z } from 'zod';

const setSchool = createAuthEndpoint(
  '/schools/set-school',
  {
    method: 'POST',
    body: z.object({ schoolId: z.string(), name: z.string() }),
  },
  async (ctx) => {
    const { schoolId: id, name } = ctx.body;

    await ctx.setSignedCookie(
      'school',
      JSON.stringify({ id, name }),
      ctx.context.secret
    );

    return ctx.json({ success: true });
  }
);

export const schools = () => {
  return {
    id: 'schools',
    endpoints: {
      setSchool,
    },
  } satisfies BetterAuthPlugin;
};

'use server';

import { auth } from '@/lib/auth';

export async function action() {
  const result = await auth.api.setSchool({
    method: 'POST',
    body: {
      name: 'Default School',
      schoolId: 'default-school-id',
    },
  });

  console.log(result);
}