I'm not sure what caused it, but notifications for Facebook Messenger on my iPhone 8 are no longer showing up anywhere (no badges, app icons, or notifications of any kind). However, when I open the Messenger app, I guess it triggers something as at that point it at least updates the badge icon:
I've enabled all notification settings I can think of, yet still no notifications.
In the Messenger app:
And under Settings > Notifications > Messenger:
I'm on the latest version of iOS (14.3) and my Messenger app is up to date (294.0). This seems to be specific to the Messenger app as I receive notifications from other apps (e.g. Messages, Slack) just fine.