This is what worked for me:
- Open Snipping Tool normally via the start menu to get the UI up
- Click the three dots in the top left and click Settings
- Disable "Automatically save screenshots"
Caveat that this is in/after updating to Windows 11 for me so I don't know if this is option is in Windows 10, but I didn't even know it was a thing until I ran out of ideas and went digging. After disabling the auto save the popup started appearing for me again (I also went to check my pictures folder and sure enough there were the countless tests screen grabs I'd made!).
Apologies for no screenshots (ironic), the form keeps saying its failed if I try to upload an image.