Quality Assurance Projects - Personal Library - Cast Error

Hello,

I am working on the Personal Library project for the Quality Assurance certificate. I’m currently working on posting a comment for a book and am using the findByIdAndUpdate() Mongoose method. After successfully updating the comments property in my document, I thought it would be best to also update the commentcount property inside the same method. However, doing this returns the following CastError:
CastError: Cast to Number failed for value "{ '$size': '$comments' }" (type Object) at path "commentcount"

Book Schema

require('dotenv').config();
const mongoose = require('mongoose');

const bookSchema = new mongoose.Schema({
  title: {
    type: String,
    required: true
  },
  comments: {
    type: [String],
    default: []
  }, 
  commentcount: {
    type: Number,
    default: 0
  }
});

const Book = new mongoose.model('Book', bookSchema);

//**********EXPORTS**************
exports.Book = Book;

API

app
    .route("/api/books/:id")
    .post(async (req, res) => {
      let bookId = req.params.id;
      let comment = req.body.comment;

      if (comment) {
        console.log(`COMMENT: ${comment}`)
        try {
          let book = await Book.findByIdAndUpdate(
            bookId,
            {
              $push: {comments: comment},
              $set: {commentcount: {$size: '$comments'}},
            },
            {new: true}, 
          );

          console.log(book);
          return book ? res.json(book) : res.send("no book exists");
        } catch (err) {
          console.error(err);
          return res.send("no book exists");
        }
      } else {
        return res.send("missing required field comment");
      }
    })

Does anyone know why I’m catching the CastError and a possible workaround?

P.S. I know that I can just push the new comment to the document, then use the returned, updated book to set commentcount to the comments length, and then do book.save(), but I would like to figure out why it is not working using the $set operator with $size.