Mongoose not returning queried elements of arrray

Question

Consider the following document schema:

var WalletSchema = new Schema({
    name: {
        type: String,
        required: 'Kindly enter the name of the Coin'
    },
    .
    .
    .
    coins: {
        type: [CoinSchema]
    }
});

var CoinSchema = new Schema({
    name: {
        type: String,
        required: 'Kindly enter the name of the Coin'
    },
    symbol: {
        type: String,
        required: 'Kindly enter the symbol of the Coin'
    }
    .
    .
    .
});

Now consider the following function:

exports.edit_coin = function(req,res) {
    Wallet.findOneAndUpdate(
    {
        name: req.params.wname,
        "coins.symbol": req.params.symbol
    },
    {
        $set: {
            "coins.$": req.body,
            last_updated: Date.now()
        }
    },{
        new: true
    },function(err,wallet) {
        if (err)
            res.send(err);
        console.log(wallet);
        res.json(wallet);
    });
}

I only want to see elements of the coins array which are equal to the given symbol (req.params.symbol).
When I run the function with req.params.wname = Wallet, which is a wallet in my DB which has two coins in it one GOC and one BTC, and req.params.symbol = BTC with some JSON as the body I expect to only get BTC on console, but the following is what I get:

{
    "_id": "61d2e17ebc07b26e3f3f692a",
    "name": "Wallet",
    "balance": 1042.8,
    "coins": [
        {
            "name": "Go coin",
            "symbol": "GOC",
            "amount": 4,
            "rate": 21.4,
            "_id": "61d2e21a4b112f01592613d0"
        },
        {
            "name": "Bitcoin",
            "symbol": "BTC",
            "amount": 2,
            "rate": 50000,
            "_id": "61d2e77c76fd08ea50a3aff5"
        }
    ],
    "last_updated": "2022-01-03T12:09:32.242Z",
    "__v": 0
}

Why don't I only get bitcoin?