It’s wild that you can’t do the same thing to get the same result for two different accounts.
I don’t use a security key for FB, but I see this option in:
Desktop web browser (FF): My picture on the top right → Settings & Privacy → Settings; In the left panel, Accounts center → Password & Security → Two Factor Authentication → My picture → Additional Methods → Recovery codes
Android App: 3 bars on the top right → Setting & Privacy → Settings → Seee more in Accounts Center → Password & Security → Two Factor Authentication → My picture → Additional Methods → Recovery codes
So, pretty much the “same” path for both apps. Hope they work for you.