I was just wondering what the process was to unlock these? I know the steam version you get them in the library for owning the previous games, but I have 3 (Steam) and 4 (GOG) installed and still don't see anything in the library. Does it just look for the game files in common install locations?

The weapons unlock in the library after you beat the game on all platforms except Steam where you get them initially if you own the previous games.

Yeah, I found that looking around myself. I was mostly wondering if there was a way to get it earlier for owning the previous games on other services outside of hacking my save or something but I'm betting it gets what games you own directly through the Steam API or something (I don't know if steam can actually do that, I'm just guessing; I know saves and having the games installed doesn't seem to make a differences, nor does Galaxy).

It probably does in fact check if you own it via a Steam API request, either GOG Galaxy doesn't have similar functionality or they just didn't bother implementing it (less work since they probably use the same DRM-Free release as itch.io)

Going to add to this topic now that I've beaten the game: For anyone who feels like they might be missing out on not getting the weapons early, in the long run they don't really matter. They're basically just easter egg weapons that are fully reskins of other weapons you get in the game with the same damage and movesets.