No, as MacsBug said, "Apple has not made Save to photos an option as of yet." on macOS.
Personally I wouldn't want that, I prefer to save to the Desktop where I can edit with Markup or Preview as most of my screen shots are for sharing/posting to other web sites or sent by email as attachments. If they went to Photos I would have to open the app, copy to the Desktop then quickly delete the original to prevent it syncing to iCloud and all my other devices when I really only need one local instance of the image.
If I decided to keep the screen shot, storing it in a dedicated folder is a better method. I have only one folder on my Desktop, it's called "Temporary Desktop Items" which I use for that purpose. If, on review I decided to keep the image I can always drag it to the Photos icon on the dock to import it.
You can do a similar thing on an iPhone by clicking on the image and choosing to Share it to Files which I have done and created a Folder Called Screen Shots in Files which also appears in the iCloud Drive folder in Finder on my Mac. Prior to that my iPhone Photos app used to fill up with screen shots of receipts, documents, business cards ect. Now they are all in one place and Photos is only filled with photos.