How do I query to fetch number of Posts made by a User using mongoose?

Question

So I'm trying to fetch the total number of posts done by a specific user.

Models

Post.ts (In post model I have user ref)

user: {
      type: Schema.Types.ObjectId,
      ref: "User",
      required: [true, "Please provide user ID."],
    },

I tried

const posts = await Post.find({ user: req.user._id});
const postCount = posts.length;

But I want to aggregate the User so I can get the user data along with the post counts. what I tried is below but I'm getting 0 number of posts.

const user = await User.aggregate([
      {
        $lookup: {
          from: "post",
          let: { userId: "$_id" },
          pipeline: [{ $match: { $expr: { $eq: ["$$userId", "$userId"] } } }],
          as: "posts_count",
        },
      },
      { $addFields: { posts_count: { $size: "$posts_count" } } },
    ]);

I searched but couldn't find any related answer.