While the game installs fine, and even allows you to get through creating a character, you'll see at most first several seconds of the opening cutscene before an error boots you back to the title screen.

Tested on Proton 7.0-1, Proton Experimental, and Proton Experimental [Bleeding Edge].

Additionally, I noticed issues with the in-game web browser that handles account sign-in and another informational screen prior to character select. When the game is fullscreeened, these screens can appear entirely black until refocusing the window. But even then, serious flickering occurs. This can be mitigated somewhat by letting the game remember your credentials to bypass these windows on subsequent attempts, or by playing in windowed mode.

The various errors I've received are: 01-0005-0302-00 A connection error has occurred. 01-0002-0113-00 A session error has occurred. 01-0052-0062-07 Unable to send data.

None of these mention EAC outright, but given that none of these show up when accessing the game from a second machine running Windows it seems pretty clear that the anti-cheat is to blame.