As one of the weird people who did not like Firefox using OS's default notification system due to how obnoxious and disruptive they are (the popup is actually larger than Firefox's old Web Notification popup, there's a dead zone AROUND the notification that can intercept clicks without doing anything at all.)
So, here's a better idea: Keep the old Web Notification system, preferably add a setting for quick switching, and add a new side panel to not only see the notification history, but ALSO separate them by source (Which site the notification comes from, for example) and keep the history for as long as the user wants or even allow them to set an expire date to them based on source (so, say, I could set it so Youtube's notification lasts in the history only until Firefox is closed, and GMail's could last 30 days or until I manually remove the notification).