I'm thinking about what could be integrated with Nintendo Switch and I came up with these things

1) Showing what game you're playing right now. As this works already with friends on Nintendo Switch, I think this might be doable.
2) Games library. Might need to integrate manually or by playing them as the public profile only shows the last 20 games played and I think the library (eshop games and cartridges combined) is saved on hardware.
3) Friends list. Being able to see who is online, what they are playing and when someone was online the last time. Maybe even manage you friends list, but I guess that's a thing for the future if other more important stuff was added.
4) Play time of games. This is an odd thing with the Switch as the information Nintendo provides is very inaccurate with "XY hours or more" or "First played X days ago" (see picture). So one way would be to just take what you get by Nintendo and state the hours given by Nintendo. So in this example, Xenoblade Chronicles 2 would just show 200 hours while Super Mario Maker 2 and Rocket League won't have any information about play time at all.
The other way would be to just import the hours Nintendo provides for a start when played a game the first time while the Switch is connected to GOG and from then on let the time being tracked by GOG itself to get a more accurate time.
5) Browsing the eshop and buying stuff. As you can do this on any device with a browser already, this should be easy to integrate once (and if) GOG decides to implement stores.

So the things that obviously won't work:
1) Achievements. As Nintendo doesn't provide those.
2) Chat. As Nintendo doesn't provide that.

So I think this is as far as it goes. If anybody got more ideas, I'd love to hear them :D