(last time I checked at least, it was not).
It doesn't, although
it could do.
One mistake and your identity is linked back to the mixed coins. Does anyone here have some sort of documentation on that?
A must-to-do tactic is coin control. To link yourself and your mixed coins, you have to either spend mixed and unmixed UTXO in one transaction or via change.
ChipMixer does have some good practices, but that implies you'll use their service (which provides better mixing than a coinjoin, but trades-off self-custody):
http://chipmixorflykuxu56uxy7gf5o6ggig7xru7dnihc4fm4cxqsc63e6id.onion/articles/best-practices-2021 (use Tor)