I think mixers are easy to detect when the transaction either comes directly from e.g. a CoinJoin or from a known mixer's wallet. I've never studied mixing heuristic analysis but I think it's not impossible to find at least few of the addresses a mixer owns?
Anyway, I think the easiest way to hide this history is just bouncing your mixed BTC from address to address. After a few days of every-now-and-then bounces, I doubt anyone will have a clue. Perhaps this is a tactic also used by mixers?
I'd be curious to know the answer as well. There most likely still are patterns through which they can find the origin of an address's coins.
I think coinjoin detection might be a bigger issue than it was before with the new taproot update. And I am sure there is a algorithm to generate new bitcoin addresses so that you can't link the new addresses with mixer owned-addresses.
But then again, I am no heuristics analyst either. But I do have faith in the community developing better ways of sustaining bitcoins anonymity. Otherwise the governments and regulators would already have ruined the game for us.