How to aggregate with many conditions on MongoDB. Double $lookup etc - node.js

Question

How to display "hardest category" based on in which "study" size of notLearnedWords was the highest. MongoDB Aggregation
I have these 3 models:
Study
WordSet
Category
Study model has reference into WordSet, then WordSet has reference into Category.
And based on Studies i'm displaying statistics.
How i can display "The hardest category" based on size of "notLearnedWords" was the highest?
I don't know on which place i should start with that querying.
For now i display "hardestCategory" as element that is most used.
I think that condition would look something like this:
{ $max: { $size: '$notLearnedWords' } } // size of the study with most notLearnedWords
I would achieve a response like this:
"stats": [
{
"_id": null,
"numberOfStudies": 4,
"averageStudyTime": 82.5,
"allStudyTime": 330,
"longestStudy": 120,
"allLearnedWords": 8
"hardestCategory": "Work" // only this field is missing
}
]
I've tried to do it like this:
const stats = await Study.aggregate([
{ $match: { user: new ObjectID(currentUserId) } },
{
$lookup: {
from: 'users',
localField: 'user',
foreignField: '_id',
as: 'currentUser',
},
},
{
$lookup: {
from: 'wordsets',
let: { wordSetId: '$learnedWordSet' },
pipeline: [
{ $match: { $expr: { $eq: ['$_id', '$$wordSetId'] } } },
{
$project: {
_id: 0,
category: 1,
},
},
{ $unwind: '$category' },
{
$group: {
_id: '$category',
count: { $sum: 1 },
},
},
{ $sort: { count: -1 } },
{ $limit: 1 },
{
$lookup: {
from: 'categories',
localField: '_id',
foreignField: '_id',
as: 'category',
},
},
{
$project: {
_id: 0,
category: { $arrayElemAt: ['$category.name', 0] },
},
},
],
as: 'wordSet',
},
},
{
$group: {
_id: null,
numberOfStudies: { $sum: 1 },
averageStudyTime: { $avg: '$studyTime' },
allStudyTime: { $sum: '$studyTime' },
longestStudy: { $max: '$studyTime' },
allLearnedWords: {
$sum: { $size: '$learnedWords' },
},
hardestCategory: {
$first: {
$first: '$wordSet.category',
},
},
studyWithMostNotLearnedWords: { $max: { $size: '$notLearnedWords' } },
},
},
]);
Study
const studySchema = new mongoose.Schema({
name: {
type: String,
},
studyTime: {
type: Number,
},
learnedWords: [String],
notLearnedWords: [String],
learnedWordSet: {
type: mongoose.Schema.Types.ObjectId,
ref: 'WordSet',
},
user: {
type: mongoose.Schema.Types.ObjectId,
ref: 'User',
},
});
WordSet
const wordSetSchema = new mongoose.Schema({
name: {
type: String,
},
category: {
type: [
{
type: mongoose.Schema.Types.ObjectId,
ref: 'Category',
required: true,
},
],
},
});
Category
const categorySchema = new mongoose.Schema({
name: {
type: String,
},
});