Make sure that "Do Not Disturb" is not switched on (you can find the icon in the top right of your notifications panel).
I found that if DND is switched on, the snipping tool would auto minimise after taking the screenshot.
As soon as DND was turned off, it would pop up in front of other windows as I would expect.
**EDIT: Nevermind... it's stopped working again GRRR.
**EDIT 2: Oh, it does work BUT there is more to it. By default windows 11 is set to automatically turn on DND when using an app in full screen mode. As Snipping tool runs in full screen mode, it is turning DND on its self! To fix it go to:
Settings --> System --> Notifications --> Turn on do not disturb automatically
And make sure that "When using an app in full screen mode" is NOT checked.