You can go to the desktop mode and install the GOG launcher. Then after installing your games, open Steam and add the games as non-Steam games. They'll show up in game mode as well.
The Heroic Launcher can add your games from GOG, EGS, and some others iirc to Steam automatically. I believe there are other, supposedly better options too, but I can't remember the name(s) right now. Also don't remember what (if anything) was wrong with Heroic.
Haha yeah there are still a couple oddball things like battlenet I use lutris for, but damn if heroic isn't just easier all the way around.
I've never gotten past the "well I tried once and it didn't work" stage with bottles, maybe one of these days I'll actually sit down and try to get it working properly.
Bottles is really just a really nice UI for managing wine/proton. If you already know what you want/need to run something, it's a breeze to set up in bottles. And even if you don't, trying the various tricks that exist to get something running is made easy.
I can't say the same for lutris. It can do all the same things and even more, I just don't like the UI/UX, at all. It can do tons, but IMO it's not the best tool for any of it.
On bottles, the more you actually understand about how wine/proton can be configured, the more sense bottles will make.
Heroic launcher is pretty good alternative. It has a feature to "automatically add to steam" as well that should make a link in the big picture steam deck mode so you don't have to drop to desktop mode to make them work as well.