Cannot sync iPhone contacts with Facebook [iOS 12]

The title is self-explanatory. All recent online tutorials (like this one) tell me to go to Settings -> Facebook -> Update All Contacts, but this option simply doesn't show up for me. Actually the whole section "allow these apps to use your account" doesn't show up.

Has anybody encountered similar problems and managed to circumvent them?

Trigger the Facebook app for uploading the contacts. Then iOS asks for permission and you might be able to see the settings. Also check contacts settings in Settings → Privacy → Contacts to see if Facebook ever asked for the contacts or not.