Possibly since those coins are already linked to you via Binance. Should coinjoin it prior to sending it to your cold storage wallet
Discussion
Yeah, also if you KYC’d with Wallet of Satoshi that’s not really helping much.
and what if I do the lightning withdraw directly to my self-custodial wallet? Shoud I do a swap after that?
The coins would still be linked to you even if you did a lightning withdrawal. In either case before you put them in your self custody wallet, you should coin join them for maximum privacy should you choose this route. Or simply have two different wallets one for kyc bitcoin and the other for nonkyc bitcoin transactions