It seems like there's a glitch somewhere in their system that is causing these accounts to be inappropriately flagged. EA has enabled EAC support for Linux, so there's no ToS reason why playing on Linux would get you banned. If they didn't want Linux players, they could have just disabled the Linux version of EAC.
It's possible they want to support Steam Deck without supporting the rest of linux desktop, which would just be... dumb. The Steam Deck, in Valve's own words, is "just a PC" anyway.
Considering they unbanned all most of the linux users last time though, this is likely just another mistake.