I also noticed that behavior. I was used to taking perhaps 2 or 3 snips in succession and having the Snipping Tool show them in separate windows that I could return to later.
The solution I found was in the Snipping Tool settings. Enable "Multiple windows" - "Open new screenshots in different windows".
However, I agree that the tool is broken at the moment in that the Snipping Tool window does not pop-up automatically. The pop-up notification shows at the bottom-right but an extra click is required to force the window to open with the screenshot. I first noticed this a while ago when using the Win Key + Shift + S keyboard shortcut but as I normally use a right-click on the taskbar Snipping Tool shortcut to take a new snip (immediately or with a delay) and this used to behave perfectly (presenting me immediately with a Snipping Tool window) I wasn't too annoyed by it.
Another bug which I've seen since first using Windows 11, is that even when the Snipping Tool window popped up automatically, it's position on the display bounced around all over the place. In other words the tool would not remember the size and position of the window unlike almost all other Windows applications I can think of. This is still the case today.
Finally a relatively minor change compared with the Windows 10 version is the lack of an "Open with" option. In Windows 10, with the Snipping Tool editing window open, I could click the 3-dots menu and click "Open with". I could then select another image editing application to edit the screenshot. When done and saved, I could then simply close the Snipping Tool window. Instead there is an "Edit in Paint" option shoe-horned into the menus at the top of the window and standing out like a sore thumb. The new Paint is okay but if I want to use my preferred image editing application, I have to save the snip and then open it in the other application. This is no big deal but yet another little annoyance.
There are some nice enhancements such as the screen recording (although as others have noticed, this feature seems to have broken the automatic window opening), the 5 second delay (previously it was just 3 or 10), and the OCR option (although I tend to use the Power Toys keyboard shortcut for this at the moment), it's frustrating that Microsoft don't seem to listen to valuable feedback as presented in this forum and address obvious bugs.
Shaun.