NextJs & Mongoose putting a jwt in database - node.js

Question

I tryed myself on a little NextJS App with Mongoose and JWT (json web token).
Everything works and I can put user into my database and other stuff. Just when I create a JWT I can't put it into my database. Here is my code, grateful for every help :D
First my schema for mongoose:
const mongoose = require('mongoose');
const UserSchema = new mongoose.Schema({
username: {
type: String,
required: [true, 'Please add a title'],
unique: true,
maxlength: [15, 'Username cannot be more than 15 characters']
},
password: {
type: String,
required: true,
maxlength: [100, 'Password cannot be more than 100 characters']
},
jwt: {
type: String,
required: true,
maxlength: [1000, 'JWT cannot be more than 200 characters']
}
})
module.exports = mongoose.models.User || mongoose.model('User', UserSchema);
I don't know if type: String for jwt is correct, but JSON looks weird too and doesn't work.
Now my backend API Code:
import dbConnect from '../../../utils/dbConnect';
import User from '../../../models/User';
import sjcl from 'sjcl';
var jwt = require('jsonwebtoken');
const hashword = "censored"
dbConnect();
export default async (req, res) => {
var passwordtohash = req.body.password + hashword
const BitArrayHash = sjcl.hash.sha256.hash(passwordtohash);
const passwordhashed = sjcl.codec.hex.fromBits(BitArrayHash)
var bodywithhash = req.body
bodywithhash.password = passwordhashed
const { method } = req;
switch(method) {
case 'POST':
try {
const user = await User.find({"username": bodywithhash.username, "password": bodywithhash.password});
if (user.length > 0) {
createJWT(user);
res.status(200).json({ success: true })
} else (res.status(200).json({ success: false}))
} catch (error) {
res.status(400).json({ success: false });
}
break;
default:
res.status(400).json({ success: false });
}
}
async function createJWT(user) {
jwt.sign({
exp: Math.floor(Date.now() / 1000) + (60 * 60),
data: 'foobar'
}, 'secret')
const iduser = { "_id" : user[0]._id.toString()}
const updateuser = await User.findByIdAndUpdate(iduser, jwt);
}
All my users in the database have a default value for JWT called "default"