EAC doesn't work with wine/proton. So if you run any windows game under linux with wine/proton that requires EAC, it will not work.
I haven't tried the native linux client with eac, since i only play on private servers with friends, where we usually disable eac anyway.
What do you mean by "microsoft ones"?
The native client implements eac on his own, or it doesn't. There is no connection to any microsoft stuff.