to be honest I'm not even sure now even the dex because if you withdraw btc and eth from dex and cash out going to your bank, it may be traced still going to you.
Authority is less your problem and in fact, Any business establishment like banks will give your bank details once they request since they are the Authority and they will not ask for it unless you do something unlawful like thief.
Let's face the reality, You can't keep your privacy safe as long as you are converting your BTC in Fiat because all transactions will end in the bank or similar platform that holds your KYC since its Fiat. Almost 90% of crypto user are trading back there asset to Fiat to take some profit.