How can I scan my iPhone for virus?

Your cache files had been corrupted and does happen without any exploit on your device. Another time you will see this corruption in the cache files is when you see multiple app icons on the screen for the same app. That is also why you saw that Facebook had not been removed from your device, because the cache files thought it was still there, and you were not able to open the app. Doing the Force Restart clears these cache files and I actually recommend doing it after every update as that is where the corruption usually happens.

After the Force Restart, I suspect your phone is working normally and if there still is a problem with the Facebook app, you should now be able to delete it and redownload. I don't think it is necessary to do the Backup/Restore as that is just another way to clear those cache files that you have now done with the Force Restart. If we cannot convince you that you don't have an exploit on your device, then you would need to do a Factory Reset and set the device up as new. This will completely wipe your device and all data that is not stored in iCloud will be lost. The Backup/Restore just places your device in the exact same state as before the Factory Reset and also clears those cache files.

Specifically for the Facebook app, Meta just sent out another update 1 hour ago where they claim it has fixed some bugs and resolved crashes that users had reported. It is version 503.0.0. That is the most recent update for the app, along will 10 previous updates for it in just the last month. After any Facebook update, there is a potential to see problems with the app, as there is very little testing for these bugs before the update is released and it is apparent by the number of updates they have to fix bugs, that they are relying on their users to test the product.