Your wallet’s list of addresses is generated by your xpub (extended public key).

If that xpub (and all of its addresses) have been leaked, then any address you use will be linkable (with some effort) to that initial KYC’d transaction.

I don’t believe you can infer an xpub from a wallet address (although I could definitely be wrong about that, so #asknostr), but your watching wallet software (and I maybe even the node you broadcast transactions to?) can see your xpub/addresses.

So if you use Ledger Live, for example, then Ledger does know all of your addresses. It would take coordination between Ledger and the exchange to dox all of your addresses, but it’s possible in a way that doesn’t exist when you have a separate, KYC-free wallet. (Highly recommend).

The other difficulty (which I think you’re covered in when emptying a wallet) involves change addresses. You can end up accidentally doxxing your stack if you “share” a wallet because of how UTXOs are managed.

It’s 1000% better to have separate wallets, separate stacks, to never need to worry about this.