Specialist software in general is patchy at best. There are often FOSS alternatives... But in the same way they aren't compatible with what other people are using.

I game on Linux and mainly play games bought from GOG. Both GOG and Epic games are extremely easy to get working, and are as simple as downloading Heroic Games Launcher, signing into GOG and/or Epic, and choosing the game you want to download from your library. While it is possible to use the official GOG Galaxy client with Lutris and WINE, I personally don't recommend it, as it's quite a glitchy and laggy experience, and is only done by people who can't live without GOG achievements. For GOG.. just use Heroic. It's just as easy to use as the official Galaxy client is on Windows and also supports cloud-saves.

I've never used Amazon, but Heroic also recently added downloading your Amazon Prime games as an option, which I imagine is just as easy to get working as GOG and Epic Games already are.

This part isn't necessary, but if you want to play those games but launch them from Steam, you can add each game individually to Steam as a non-steam game through the Lutris or Heroic Games' interface. A handy app I recommend, which I never hear people mention, is BoilR, which automatically adds all of your non-steam games in bulk into your Steam Library.

As for the EA App and Ubisoft Connect, I ditched them over a year ago due to not wanting to support the companies (same with Epic). I honestly don't remember what the process was exactly for those launchers, but I do remember it was very easy to set up in Lutris.

Lastly, I've never used Battle.net either, but I've heard it's quite easy to set up in Lutris.

You can search on e.g. Lutris if the game is supported. It's usually just a one button install

Fairly easy with something like lutris or the heroic game launcher if said games are on gig amazon gaming or epic