You can just batch the screenshots and then switch to the photos app for the extraction. I’m still failing to see the problem.
The iPad can use apps in multiple floating windows, there’s no difference here. You don’t have to switch back and forth between apps.
You can even use a keyboard and mouse and the same copy paste keyboard shortcuts if you really want.
And I’m sure there are apps on the App Store to help this workflow in some way. The iPad isn’t some static device where you’re stuck with the software it comes with.