We had this problem and this fixed the issue for us.
Press Shift+Win+S to start the snip. Snip a portion and it will pop up the notification in the bottom right corner with what you snipped. Click that pop up notification. For me, after clicking that, it popped up a dialog asking which "snipping tool" to use to open it. Both said snipping tool, only the second one had the snipping tool icon. I clicked the one with the snipping icon and clicked "always". It then opened. I closed it and now using the snipping tool without using the keyboard shortcut also returned to normal. Meaning, I can start the app with my mouse and snip a portion. It would be minimized after snipping, but when I click it, the image is there where I can copy, edit and/or save.
It looks to be a bug in the latest update where the program tries to open the image with the old snipping tool version, but can't as it doesn't exist. When I choose "always" with the second option, it told Windows to use the newest version and fixed it... at least that's what I think happened.
I hope that helps someone.