It's a good point Boo Nagatsuka, but in my case I've never enabled Focus Assist. I think whenever I've used the Windows key + Shift + "S", a notification always popped up for me and if I clicked "Select here to mark up and share the image" I could edit it if I liked or ignore or dismiss it and just paste ti somewhere a little later on. (Actually in Win 11 right now the notification did pop up even with Focus Assist enabled and in Win 10 it doesn't pop up only if 'Alarms only' is enabled). My gripe was that if I right-clicked the Snipping Tool taskbar icon (in Win 11) and clicked "Take a a new screenshot" I expected the editor window to appear instead of a notification (because it would then be superfluous) and when I only got the notification with no editor window I became a little irritated that it wasn't behaving as I was used to it behaving particularly in Win 10.
The fix as I've detailed earlier is in Apps-> Default Apps-> Screen Snipping switching Snipping Tool off and making "Screen Snipping" the default app for MS-SCREENCLIP - the logic still eludes me but it works. Annoyingly (as you've found with Focus Assist) Microsoft sometimes switch this back so I now know the sequence very well.