Contacts showing up in new texts, but not in Contacts app (or anywhere else)

A couple weeks ago my phone deleted names attached to numbers in phone calls and texts. So all previous calls and text messages have no names attached to them.

BUT (!!) when I start a new text, all the contacts (even email addresses) show up when I start to type in names in the “To” field. Those names then disappear again when I write the actual message.

I have tried all of the usual fixes — checking the “Groups” settings in contacts, checking iCloud, force restarting the phone, resetting network settings. Oddly, some contacts are still in Contacts, but it’s really random and only about 10% of them.

Is there a way to recover theses lost contacts? There are clearly in here somewhere.

See the pictures below to see a great example: