I don't think Tolkien wanted to explain, or decide who Tom was, he was an enigma and the only explanation is in Tom's own word to Frodo.
Something significant is that Tom said he was there (in Middle Earth) before the Dark Lord came from outside, I think he was referring to Morgoth, not Sauron, as he also said he was there before the elves went to the west.
Now, if we try to find an explanation in the books, or in Tolkien's letters or notes, we won't find any, but in the general context, it seems to me he was a maia.
We know the maiar were spirits, and there many of them, some were very powerful like Eonwe or Arien, and some were less powerful.
Of all the creatures defined in the Tolkien's books, Tom would only fit in the maiar category IMO. But that's only speculation of course
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