The EA launcher works just fine via Lutris. Source : I’m using it to play Mass Effect Legendary Edition perfectly fine.
Battle.net works as well, OW2 plays fine on Linux.
GOG & Epic work through Heroic Launcher as you mentioned.
As for a distro, I’d aim for something Arch based. Simply because you’ll get the latest drivers and mesa versions all the time, which is proven to increase FPS a ton over say, Ubuntu.