Can't add anyone to my contacts

iPhone X, latest iOS. For quite a while now I've been unable to add a new contact. I thought I was constantly being "old" in that I'd add a person and their phone number, but could never find them later. But just now I tried it and it doesn't work, although the contact is IN the phone (which is to say when they call all their info, including address and mother, show up when I check the information on "recent calls"). I can even take this info and add it to my "Favorites", but when I go to find it via the alpha general contact lookup I can't and there is no additional contact added (the number stays at 78, although the favorites list has increased and their number is indeed there).

My phone has been rebooted since this first happened with no change. Anyone here of this before? And have any workaround (other than adding them all to "My Favorites". Sigh).