What happened?
I’ve always been able to search Google Photos by a person’s name or if don’t know name can just search for all photos with a selected person’s face.
Searching by a person’s name or face is gone on all my devices.
Account in good standing and everything else works ok.
Sorry, can’t help much. Still works fine for me. Last updated 25th September. It mentions last update included a new search tool for identifying unwanted photos. Maybe I’ll switch off auto update, because if what you describe is due to a new update I don’t want it. Btw running Android 8.0 
Got a prompt when I logged in to Google Photos on a browser asking if I want to turn the face search feature off. I clicked keep it on, but I don’t see that option in the settings now that I go back to it. Not sure what it’s about.
Yeah, I got that too, within the last couple of days. If you click to turn it off, there’s a confirmation screen asking if you really want to delete existing faces (or something like that, I did it accidentally and only saw it for two seconds). Maybe that’s what OP did.