DrDm: It never gave me the option to select a file path or anything. It's just straight up not on my computer after installation. I now have less space on my hard drive, so clearly those files are somewhere but I can't find them despite searching extensively. Thanks for the replies my dudes but I'm giving up because this problem just doesn't even make sense.
I am assuming here you are using a Windows PC. If you are a Mac user, I can't help because I know nothing about Macs, nor want to learn anything about them.
First of all, did you download the offline backup installers with the GOG Galaxy client, or a web browser? EDIT: Ok you said later you used Galaxy, fine.
As I don't use the GOG Galaxy client myself, I do not know where GOG Galaxy downloads the offline installers (if you chose to download them with Galaxy; I guess the download folder is mentioned somewhere in the GOG Galaxy client options), but most if not all web browsers (Edge, Chrome, Firefox) download files by default into your Windows Downloads folder.
So, open File Explorer and head to your Downloads directory, maybe you see your downloaded GOG installer files there.
If you are still wondering why there are two ways to download and install GOG games (the "offline backup installers" and clicking on that magic Install button on the GOG Galaxy client), the "offline backup installers" are the original way how GOG games were provided by this store. You downloaded the installer files with your web browser or a separate downloader application, and then installed the game just like you'd install any normal Windows program that is provided in an installer format.
The GOG Galaxy client came later for people who find that old way too "archaic" or "cumbersome" and want Steam-like features like automatic updates, cloud saves and social features. Still, many of us prefer using the original offline installers because they are easily archivable, and are fully usable even in the future if and when the GOG store closes its doors for good. When you have those installers on your hard drive, installing and playing those games doesn't depend anymore on the existence of the GOG store/service.