The design of the notification system suggests to me that Apple believes that the user should drop everything and respond to notifications immediately, or at least, in the very near future (and if you don’t do that, it’s user error again!).
In my macro to Dismiss notifications about Sequoia, I use OCR to get the text content of notifications. I wonder if you might find it helpful to do the same, and then copy that text to an alert system or log of your choosing.