The most efficient way to handle one to many relationship in MongoDB

Question

Let's say I have a one-to-many relationship - A user has many todos. I want to be able to perform the following:

• Give me a specific user without the todos
• Give me the todos belongs to a specific user
• Give me a single todo by id
• Add, update, and delete todo

I can tackle it in three ways:

Embedding the todos inside the user document

 import { Schema, model } from 'mongoose';

 const userSchema = model('User', new Schema({
   name:  String,
   todos: [{ title: String, id: String }],
 }));

Use Todo Ref

import { Schema, model } from 'mongoose';

 const userSchema = model('User', new Schema({
   name:  String,
   todos: [{
    type: mongoose.Schema.Types.ObjectId,
    ref: "Todo"
  }],
 }));

 const todoSchema = model('Todo', new Schema({
   name:  String
 }));

Use Todo Id

 import { Schema, model, ObjectId } from 'mongoose';

 const userSchema = model('User', new Schema({
   name:  String
 }));

 const todoSchema = model('Todo', new Schema({
   name:  String,
   userId: ObjectId
 }));

What will be the most efficient way to handle this scenario in MongoDB? Adding an index on the userId property in the last solution will make the query faster?