In addition, the movement of large transactions always attracts If the OP buys a small amount, I doubt it will attract attention.

Someone said that sooner or later we might accidentally run into dirty bitcoins, but again, large transactions are most interesting for tracking authorities.

I don't think the history will affect your purchase. It's actually been happening for lots of times but since you aren't involved in such criminal activity, you shouldn't be bothered about the it but if you seek assurance, then you could check it and buy from a different trader if that will give you peace of mind. You just have to make sure that you're purchasing from an exchange and not from an unknown person from other platforms.

How would anyone know if those specific coins were used in any illegal activity?

Use decentralized exchange e.g. Bisq don't use the centralized one that ask your KYC.