Subdocument not being saved in its own collection - Mongoose - mongodb

Question

I found this on the documentation for mongoose:
Subdocuments have save and validate middleware just like top-level
documents. Calling save() on the parent document triggers the save()
middleware for all its subdocuments, and the same for validate()
middleware.
But that hasn't been working for me. when I call save on my parent, the subdocument doesn't get created in its own collection. Here's my code:
Cart Model
const mongoose = require("mongoose");
const cartSchema = new mongoose.Schema({
numOfSessions: {
type: Number,
required: true
},
status:{
type: String,
enum: ["completed", "active", "deleted"],
required: true
}
}, { timestamps: true, versionKey: false });
const Cart = mongoose.model('shoppingCart', cartSchema);
module.exports = Cart;
User Model
const mongoose = require("mongoose");
const Cart = require("./xxxx").schema
const Schema = mongoose.Schema;
const userSchema = new Schema({
firstName: {
type: String,
required: true
},
lastName: {
type: String,
required: true
},
password: {
type: String,
required: true,
},
email: {
type: String,
required: true,
unique: true
},
shoppingCarts: [ Cart ]
}, { timestamps: true, versionKey: false });
const User = mongoose.model('user', userSchema);
module.exports = User;
Server Side
const new_user = new User({
firstName: req.body.firstname,
lastName: req.body.lastname,
username: req.body.username,
phoneNum: req.body.phone,
userType: req.body.userType,
email: req.body.email,
password: hashedPassword
});
new_user.shoppingCarts.push(new_cart);
console.log('pushed')
new_cart.save(); //If i take out this line, this subdocument doesn't get saved
new_user.save()
.then((result) => {
console.log(result);
});
To save the subdocument, I'm having to call save on it them well. Is this how it's supposed to be? Thx :D