Are these actually free-floating pop-up messages, or are they being delivered through the Windows 10 notification mechanism?
The vast majority of notifications I'm getting these days, regardless of the app or application (outside of Office), show up as the slide out messages formerly known as toasts, and then get shuttled over to the Action Center if you don't interact with them.
The first thing I'd try, in order to determine exactly what's happening, is hitting CTRL+SHIFT+V as quickly as possible once you hear the notification announced, which should throw focus to it. If it tells you to click it, hitting enter once you have focus should do the same as a mouse click.
You may also wish to consider extending the period of time a notification displays before being shuttled to the Action Center. This can be tweaked in Settings, Ease of Access, Display Pane using the Show notifications for dropdown. I think the default is 5 seconds, and I've got mine set to 7 seconds, but you can go as high as 5 minutes. The available increments are 5, 7, 15, and 30 seconds along with 1 and 5 minutes.
If it's not being handled through Windows notifications then I have no idea, and would need to replicate it. And that would also mean that it's really a question much more about how the app works, rather than how NVDA works, so a deep dive is better done on the Chat Subgroup.
Brian - Windows 10 Pro, 64-Bit, Version 20H2, Build 19042
Any idiot can face a crisis. It's the day-to-day living that wears you out.
~ Anton Chekhov