World Trees are alive.
Though their sentience occurs less in the way we recognize biological organisms. Instead, their existence is that of an intangible, empathetic sort.
Most of the time, they don't think so much as they feel. But they do talk to ones who know how to listen.
They concentrate on feeling the same sensations that mortals and immortals experience as they tread upon their lands. It is the closest thing they can get to being human.
That said, world trees can form their own bodies out of nothing in the same way certain primordial gods can. They just choose not to because they get easily overstimulated.
Could you imagine you live your life in one place, comfortable for trillions of years in the chilly universe, and then all of a sudden you're in a much weaker and smaller body, running around and jumping haphazardly?