Now I tried shorting at binance but unlike bitfinix I actually had to "Borrow" funds at a cost despite I have sufficient USDT in wallet.
Hello you dont actually borrow funds if you want to do shorting.
When you are gonna set your order make sure that your sell order are sufficient for the leverage you are going to use such as
10x, 20x, 50x and even at 125x (for BTC)

You can refer to this image the highlighted option can help you set correct budget for your chosen leverage.
I dont advise borrowing funds cause it eats a lot of commissioned when you are doing leverage. Also tip, deposit some bnb on your future account for discounted fee when you do futures.