Why does this discussion feel so familiar...?
Well, I know this is probably the umpteenth time in the last forty-odd years since I first read LotR that I've been involved in such a discourse. A while back, there was a similar one here on the Downs:
What connection between Goldberry and Ulmo? It started with that question, but eventually went into the nature and origins of Bombadil as well. Might be of interest.
For myself, I've long believed he was a Maia, probably one of Yavanna's, who came into ME before the awakening of the Elves, and, rather like Aiwendil/Radagast, became so enamored of the land, he stayed and lost his connections to the other Ainur.