It has some effect. If you deposit bitcoin into an exchange and it's coming from an address that's associated with a hack or other criminal activity, it's more likely to get flagged. It's hard to say for sure, though. Different exchanges probably use different mechanisms.

When the state seizes the coins they are magically clean at this point and are put back into circulation via the auction process.

Not all states will respect that so yes chainanalysis software will have to be updated to account for that and it does affect the fungibility