我部署了一个next.js app，实现了会员注册功能，通过next.js API路由响应前台发来的请求，在本地环境下，发送会员注册请求成功，但是部署到vercel后出现500错误，我想分发后还要保存会员信息，请帮助我解决这个问题

// components/auths/SignUpModal.tsx

...

    const onSubmitSignUp = async (event: React.FormEvent<HTMLFormElement>) => {
        event.preventDefault();

        try {
            const signUpBody = {
                email,
                lastname,
                firstname,
                password,
                birthday: new Date(
                    `${birthYear}-${birthMonth!.replace('월', '')}-${birthDay}`
                ).toISOString(),
            };
            signupAPI(signUpBody);
        } catch (e) {
            console.log(e);
        }
    };

...

// lib/api/index.ts
import Axios from 'axios';

const axios = Axios.create({
    baseURL: process.env.NEXT_PUBLIC_URL,
});

export default axios;

// lib/api/auth.ts
import axios from 'axios';

interface SignUpAPIBody {
    email: string;
    firstname: string;
    lastname: string;
    password: string;
    birthday: string;
}

export const signupAPI = (body: SignUpAPIBody) => {
    axios.post('api/auth/signup', body);
};

// pages/api/auth/signup.ts
import { NextApiRequest, NextApiResponse } from 'next';
import bcrypt from 'bcryptjs';
import jwt from 'jsonwebtoken';
import Data from '../../../lib/data';
import { StoredUserType } from '../../../types/user';

export default async (req: NextApiRequest, res: NextApiResponse) => {
    if (req.method === 'POST') {
        const { email, firstname, lastname, password, birthday } = req.body;
        if (!email || !firstname || !lastname || !password || !birthday) {
            res.statusCode = 400;
            return res.send('필수 데이터가 없습니다.');
        }
        const userExist = Data.user.exist({ email });
        if (userExist) {
            res.statusCode = 409;
            return res.send('이미 가입된 이메일입니다.');
        }

        const hashedPassword = bcrypt.hashSync(password, 8);
        const users = Data.user.getList();
        let userId;
        if (users.length === 0) {
            userId = 1;
        } else {
            userId = users[users.length - 1].id + 1;
        }
        const newUser: StoredUserType = {
            id: userId,
            email,
            firstname,
            lastname,
            password: hashedPassword,
            birthday,
            profileImage: '/static/image/default_user_profile_image.jpg',
        };
    

        Data.user.write([...users, newUser]);

        const token = jwt.sign(String(newUser.id), 'my_private_secret');
        const expires = new Date(Date.now() + 60 * 60 * 24 * 1000 * 3);
        res.setHeader(
            'Set-Cookie',
            `access_token=${token};path=/expires=${expires.toUTCString()};httponly`
        );
        res.statusCode = 200;
        return res.send(newUser);
    }
    res.statusCode = 405;

    return res.end();
};

// lib/data/user.ts
import { readFileSync, writeFileSync } from 'fs';
import { StoredUserType } from '../../types/user';

const getList = () => {
    const usersBuffer = readFileSync('data/users.json');
    const usersString = usersBuffer.toString();
    if (!usersString) {
        return [];
    }
    const users: StoredUserType[] = JSON.parse(usersString);
    return users;
};

const exist = ({ email }: { email: string }) => {
    const users = getList();
    return users.some((user) => user.email === email);
};

const write = async (users: StoredUserType[]) => {
    writeFileSync('data/users.json', JSON.stringify(users));
};

export default { getList, exist, write };

// data/users.json

Error: ENOENT: no such file or directory, open 'data/users.json'
    at Object.openSync (node:fs:600:3)
    at readFileSync (node:fs:468:35)
    at getList (/var/task/.next/server/pages/api/auth/signup.js:31:67)
    at Object.exist (/var/task/.next/server/pages/api/auth/signup.js:45:17)
    at signup (/var/task/.next/server/pages/api/auth/signup.js:83:33)
    at Object.apiResolver (/var/task/node_modules/next/dist/server/api-utils/node.js:372:15)
    at process.processTicksAndRejections (node:internal/process/task_queues:95:5)
    at async NextNodeServer.runApi (/var/task/node_modules/next/dist/server/next-server.js:488:9)
    at async Object.fn (/var/task/node_modules/next/dist/server/next-server.js:751:37)
    at async Router.execute (/var/task/node_modules/next/dist/server/router.js:253:36) {
  errno: -2,
  syscall: 'open',
  code: 'ENOENT',
  path: 'data/users.json'
}
Error: ENOENT: no such file or directory, open 'data/users.json'
    at Object.openSync (node:fs:600:3)
    at readFileSync (node:fs:468:35)
    at getList (/var/task/.next/server/pages/api/auth/signup.js:31:67)
    at Object.exist (/var/task/.next/server/pages/api/auth/signup.js:45:17)
    at signup (/var/task/.next/server/pages/api/auth/signup.js:83:33)
    at Object.apiResolver (/var/task/node_modules/next/dist/server/api-utils/node.js:372:15)
    at process.processTicksAndRejections (node:internal/process/task_queues:95:5)
    at async NextNodeServer.runApi (/var/task/node_modules/next/dist/server/next-server.js:488:9)
    at async Object.fn (/var/task/node_modules/next/dist/server/next-server.js:751:37)
    at async Router.execute (/var/task/node_modules/next/dist/server/router.js:253:36) {
  errno: -2,
  syscall: 'open',
  code: 'ENOENT',
  path: 'data/users.json'
}
RequestId: 161d1ce4-2d12-4a36-8197-8463b6a18e70 Error: Runtime exited with error: exit status 1
Runtime.ExitError

我试着用谷歌搜索，但不能解决这个问题...无论我怎么搜索5天，我找不到任何相关的文章，所以我寻求帮助...