Yep, innoextract just unpacks the files, and I then place them into a folder in the home dir. Before I knew about innoextract I also just used WINE to run the installers, and then copied the installed files around. (btw, the apple pkg installers can also be unpacked by a combination of 7z and cpio - in case you just want to unpack one of the many GoG Dosbox games and don’t have innoextract or WINE available)
I have a folder named ~/Games - and the individual games in subfolders there. In Steam’s “add non-steam game” dialogue there’s a “browse” button, and in that one I then select the .exe file of the game. That adds it to the library, and allows selecting Proton as compatibility tool in the preferences.
I am pretty sure the Steam Client reports which games you play to Steam’s “presence” service, such that your Steam Friends can see what you are playing. I don’t know if Valve gathers that data for other purposes (but would assume they do unless told otherwise). Also, some games that ship with Steam integration in their GoG installer (e.g. Loop Hero) will even track as you playing the Steam version - even if you don’t own it there.
And yeah, there is no GoG Galaxy emulation in Steam of course, but I honestly don’t care much about achievements. The lack of cloud support in non-Steam games is annoying though, as I also have a Steam Deck and those saves don’t automatically synch…