I'm not sure if you mean monster type like separate from outsider, or defined monsters with stats that you can interact with.
The first - a distinct monster type: dragon, monstrosity, outsider, god...
Most 5e D&D makes gods a different type of thing than stuff like Demons and Devils that can be arcane patrons.
As for straight monsters there have been stats defining gods (with specific god characteristics) so they can be directly interacted with as monsters/NPCs since 1e Deities and Demigods.
Indeed. But even in those editions where they are statted in such a way that they can be killed, they're invariably reserved for being right at the very top of the very top of the challenge range. I was suggesting a much wider range of CRs, maybe going as low as CR 5 or so.
(The bit I've snipped would indeed come much closer to what I had in mind.)