Yes, there is a standardized, simple way to do what you're asking. It involves using a '.nomedia' file. Basically, when you have a folder containing some photos and a .nomedia file, that folder's content won't be automatically scanned and indexed by apps like Google Photos nor Gallery. The .nomedia file excludes that folder.
The .nomedia file is an industry-wide matter that applies to a lot of other platforms (Windows, Mac, Linux, iOS, etc.) and it isn't just photo image files. This applies to audio too, so if you have a collection of song files you don't want to be included in your VLC app or PowerAmp app autodetect, create a folder, add in a .nomedia file, and that instructs your multimedia app to skip from being automatically indexing the content inside that folder.
Use your file manager app to create a separate screenshot folder, and create a .nomedia file (just a blank document will work) in that folder so Google Photos ignores that particular folder. Or dig around in some other folders in your device, there's undoubtedly a folder containing a .nomedia file (be sure to go into your file manager app's Settings to enable hidden files/folders or you won't see them). That period at the beginning of the name is important, that's what flags the file as hidden.
https://medium.com/@mutiakun/getting-know-about-nomedia-files-on-android-a51068430e38