Mongoose: Modeling and updating many to many - node.js

Question

I'm very new to mongodb and mongoose and I'd like to know how to handle many to many relations. I know mongodb is a non-relational database, but how would I model something like Users and Groups.
A User can join multiple groups while a group can have multiple users.
My Schemas look like this:
User
const UserSchema: Schema = new Schema({
username: {
type: String,
required: true,
unique: true,
},
groups: [
{
type: Schema.Types.ObjectId,
ref: 'Group',
},
],
});
Group
const GroupSchema: Schema = new Schema({
name: {
type: String,
required: true
},
users: [
{
type: Schema.Types.ObjectId,
ref: 'User',
},
],
});
So, with an endpoint like 'users/:id/assigngroup/:groupid I would like to add an User_id to User.groups and the groupid to Group.users.
For my endpoint I do something like this:
User.findOneAndUpdate({ _id }, { $addToSet: { groups: groupId } }, { new: true }).populate('groups').exec((err, user) => {
Group.findOneAndUpdate({ _id: groupId }, { $addToSet: { users: _id } }, { new: true }).exec((err, group) => {
res.send(user);
});
})
This works tho, but the problems I encountered are:
I could still add a groupId to User.users even if the Group with this id doesn't exist. I could check this with an additional Group.findOne() before the User.findOneAndUpate but this doesn't feel like it's the best/quickest way in mongoose.
How should I handle a rollback if, for example one of the findOneAndUpdate, fails?
What I need is a clean way to check if the Group with the groupid exists, then check if the user with the _id exists and after that I can add the groupid to User.groups and the _id to Group.users (and not being able to add the same id multiple times of course). What would be the best way to do this? Using findOne/findOneUpdate mutiple times for each check doesn't feel like the right way.
Please let me know if my approach to model this "relation" is completely wrong.
Thanks! :)
Edit: I don't think it's the smart way to save a reference in both models. I removed groups from the User model. So to assign a User I just use
Group.findOneAndUpdate({ _id: groupId }, { $addToSet: { users: _id } }, { new: true }).populate('users', '_id username').exec().then(group => { });
And the easy way to get all Groups of a User would be
Group.find({
"users": new Types.ObjectId(id)
}).exec(callback);
So I don't need to update a reference twice if I assign/remove a User.