Stop press! My Windows 11 laptop has just updated itself to Build 22631.3672 and, wouldn't you know it, the original problem I posted here some months back has returned!
Namely, after right-clicking the taskbar shortcut and clicking "Take a new snip", the editor window didn't appear automatically. Instead the notification appears which I then had to click to make the editor window appear.I was indebted to Jasell's post (page 12 of this forum) of October 28, 2023 which suggested the default app for "MS-SCREENCLIP" (in Default Apps, go to "Screen Snipping") needed to be set to "Screen Snipping" rather than "Snipping Tool" for some reason that is beyond me.
I've just done this again to get the behaviour back to the way I want it and as it always was in Windows 10 Snip & Sketch. The Snipping Tool by the way has also updated to version11.2404.40.0.
These instructions worked for me. It also worked to turn off "Automatically save screenshots" in the Snipping Tool Settings.