Requesting Reliable Clipboard Application w/ History?
I can confirm, Alfred does the job.

To be sure, I double checked by testing its clipboard functionality for your requirements: partial (lasso) screenshots, fullscreen screenshots and image files. Everything works fine and shows up just as expected in Alfreds clipboard manager. Pasting inside a document works, whereas saving the screenshot from clipboard into a file using finder, doesn't work. But this is normal behavior. That said, I'm running MacOS 10.15.4 and Alfred 4.0.9 with Powerpack.

If you want to try further alternatives, you could try Copy'em Paste, Clipy and Keyboard Maestro.