I’m getting an error when I try to add value in my DataBase Uuing MongooDB

I would like to add to my Database using MongooDB values with the following code but when my code is running the data I want to add to my database does not add

const profileModel = require('../DataBase/Schema.js')


function UserTotal(userId,TotalForTheSession){
    const time = new Date();
    
    var TotalTimeUserPath = './Settings/UserDataTotal.json'
    var TotalTimeUserRead = fs.readFileSync(TotalTimeUserPath);
    var TotalTimeUserFile = JSON.parse(TotalTimeUserRead); //ready for use
    
    var theyear = time.getFullYear();
    var themonth = time.getMonth() +1;
    var thetoday = time.getDate();
    
    let DateAllTogether = `${theyear}/${themonth}/${thetoday}`
    
    async function totalTimeDataBase(userId,TotalForTheSession,DateAllTogether){
        let userData
        try{
            userData = await profileModel.modelUser.findOne({userID: userId})
            if (!userData){
                let profile = await profileModel.modelUser.insertMany({
                    userID : userId,
                    totalTime: TotalForTheSession,
                    timeDate: {
                        [DateAllTogether]: TotalForTheSession
                    }        
                })   
            }
            else if (!userData.timeDate[DateAllTogether]){
                await profileModel.modelUser.updateOne({
                    userID:userId, "timeDate": {
                        $add: [[DateAllTogether], TotalForTheSession]
                            
                      },
                },
                )
            }       
        }catch(err){
            console.log(err)
        }
    }   
    totalTimeDataBase(userId,TotalForTheSession,DateAllTogether)

The code for how my Schema in my dataBase is made

const mongoose = require('mongoose')

const profileSchema = new mongoose.Schema({
    userID: {type: String, require: true},
    timeTotal: {type: String, default: 0 },
    timeDate:{}
})



const modelUser = mongoose.model('ProfileModels', profileSchema)


module.exports = {modelUser}

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When the code is executed i’m getting this errorMongoServerError: The dollar ($) prefixed field '$push' in 'timeDate.$push' is not valid for storage.*

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The file where my data is stored in my database

{
    "_id" : ObjectId("61bd159db3daaef59378e5f1"),
    "userID" : "526166979321790466",
    "timeTotal" : "0",
    "timeDate" : {
        "2021/12/16" : 1
    },
    "__v" : 0
}

I want to add “2021/12/17” : 1 in “timeDate” value like so

{
    "_id" : ObjectId("61bd159db3daaef59378e5f1"),
    "userID" : "526166979321790466",
    "timeTotal" : "0",
    "timeDate" : {
        "2021/12/16" : 1,
        "2021/12/17" : 1
    },
    "__v" : 0
}