I play EU on linux Manjaro and/or Garuda, easy to get it working with Steam.
If you you have a problem with the update, it mostly cause the EntropiaUpdater.exe is a new file and has no rights for writing and execution. Set it and try again.
If you want to play on the Steam deck its also possible, install via steam and if it is not startable the next day, install lutris and start it with lutris.
A bluetooth keyboard is needed to get in you credentials. (onscreen keyboard doesn't work cause EU captures the controls)
For playing on the steam deck, yes, with the "new" control scheme its possible to play with a controller setup, but beware, it is still a small screen.
Cause there was an update today i traced my steps:
1. delete EntropiaUpdater.exe
2. start the client, it will download the new EntropiaUpdater.exe
3. the download will fail cause of right issues with the new file
4. reset the rights to executable and so on, start the client again