I have a Galaxy Note 9, 128GB. I've tried closing and re-starting, logging off and back on, and uninstall/re-reinstalling the entire app. I've also enabled some of the notification settings others have suggested...
When going through Settings > Notifications > I have "Show With Number" under App icon badges" turned ON (this is what I am wanting it to do ideally). Facebook is ON under All apps. When I click on Facebook, ON is on, and App Icon Badges is on. Under the ADVANCED tab on NOTIFICATIONSfacebook is on. If there is another you're specifically wondering about, let me know. For a reference, I'm not certain that other apps are working either. Pinterest, for example, appears to be doing the same thing, so I assume its a wonky setting somewhere, and NOT the FB app itself.
@GrsmRngr: Just to cover all the Notification settings bases, is everything set up okay within the app itself? (The "Verify Facebook App Notification Settings" bit on this guide breaks it down quite well. Might be worth a read of the other stuff in that guide to see if there's anything else that might help in your case too.)
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Thanks I was having the same issue and was getting really frustrated with it. But I took out my sdcard an now it's working again. Do you think it's a fault with the phone or the sdcard seems so random.