As Rachel mentioned, this currently the expected behavior. I believe that actually sending notifications to the Action Center would be quite a bit more difficult than it sounds. The notification doesn't know how to make the appropriate actions when its buttons are clicked. It just tells the WDBA which button was clicked and lets it handle the event. But we can't just guarantee that the WDBA will always be running. And if it isn't, the notification continues to hang around, but interacting with it fails to produce any effect.
I think that there is some mechanism for handling this sort of thing when the application isn't running, but I'm not sure whether it is available to us. The only documentation I can find is for UWP, and Firefox is not a UWP App. There seems to be basically no documentation whatsoever for using Toast Notifications from non-UWP apps. This is a big part of the reason we decided to use WinToast - it provides us with a documented API for creating and interacting with Toast Notifications.
Another option is to just let the WDBA run for much longer, so that the notification can persist in the action center, at least for a while. This raises some questions though. How long should it run? Is it possible for these notifications to persist across reboots? I've read some documentation suggesting that this could happen, but the WDBA will definitely not be running after a reboot.
I should note that, as currently designed, if we just let the WDBA run while the notification is in the action center, it won't send (or even save) ping data related to showing the notification until it has been interacted with or dismissed. If the user shuts down the computer while the notification is in the action center, that data would be lost forever. We would need to redesign parts of the WDBA if we want to change that.
Type: defect → enhancement
Summary: Toast Notifications are not moved to action center after clicking the “Move notification to action center” button → Move Toast Notifications to action center after clicking the “Move notification to action center” button