Hello! I'm Jen, and I'd be happy to help you out with this issue.
Please follow these steps to recover the unsaved recording from snipping tool. Press Windows + R to open the Run command window. Copy-paste this path: %LOCALAPPDATA%\Packages\Microsoft.ScreenSketch_8wekyb3d8bbwe\TempState and press enter. It should open the Recordings folder from the snipping tool.
I hope this information helps. If you have any questions, please let me know and I'll be glad to assist you further.
Best Regards!
Jen :)