I feel you don't know how an exchange work.

You need to know the difference between an exchange and a non-custodial wallet.

If you hold your bitcoin on a non-custodial wallet like electrum, you have full control over your fund. If you want to make a transaction, your wallet needs your private key to sign the transaction.
If you want to withdraw your fund from the exchange, you don't need any private key. Because you are not the one who makes the transaction. You request the exchange to make a transaction and the transaction is signed by the exchange not you. In this case, the private key is owned by the exchange.

Your bitcoin address is what you need to receive a transaction.
Let's say you want to send me bitcoin. I give your my bitcoin address and you send me bitcoin.


Your bitcoin address is different from your public key, but any one has your public key can derive your address.

Any private key can generates a 1 public key and the address is generated by that public key,