Where do 🌳Ents go after they die?

[Arvedui]

Nothing is said specifically concerning the shape of the Ents. The only explanation given is what Manwë states that Ilúvatar told him:

Behold! When the Children awake, then the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared.

The only spirits I know about from that time are the Ainur, and they are able to choose shape according to their state of mind. So why not a tree?