iOS (as well, now, as iPadOS) has a Files app. After taking a screenshot, the file can be found through the Files app.
But suppose that the point of taking the screenshot is to use it from macOS. Is there a way to see the screenshot directly on the Mac without first going through the share dance (I usually go to Notes—once syncing to iCloud completes, the file(s) will be available on Notes on the Mac, but I'm sure many other options are possible).
