Without doubt the Snipping Tool in Windows 11 is buggy. I have "Automatically save screenshots" to OFF and for Windows Settings > Apps > Default Apps "Screen Snipping", the default 'file types or link types' is set to "Screen Snipping" (NOT "Snipping Tool"). With these settings, a right-click on "Snipping Tool" (either the taskbar shortcut or under "All apps") and "Take a new screenshot", always presents me with the editing window albeit the position is very annoyingly somewhat random - this is the only Windows application in my memory that breaks the rule that says 'remember the size and position of any given window for next time'.
As for Windows key-Shift-S, this always gives me a notification "Snip copied to clipboard" but has never automatically invoked the editing window requiring instead a click on the notification itself. To begin with I found this frustrating but I've come round to thinking that I actually like this behaviour. Combined with the Windows 'Clipboard History' feature, I can quickly take a few screenshots one after the other (to, say, illustrate a little workflow) and then paste them somewhere else later on.
I also have, by the way, "Multiple Windows" set to ON. When invoked with the right-click, this enables multiple editing windows, one for each screenshot, which is sometimes handy.