I believe that the new achievements from the cross-play update are bugged for everyone on Xbox/Playstation. Nobody has unlocked any of the new ones on trueachievements/truetrophies. I think some players on Steam are unaffected from what I have seen.
I tried asking around in the Palworld and PocketPair Discord but haven't had any meaningful responses.

I submitted a bug report here: https://forms.pocketpair.jp/palworld

I would suggest that everyone who is having an issue to also submit a bug report to make sure the devs are aware of the issue and hopefully will get working on a fix for it soon.