I think ‘soul’ is not something which exists in itself - it is the idea of the essence of a thing, the thing which causes an individual life.
So theories go around that there are spiritual beings separate from the physical (debatable) and I personally think that it extends to all life, such that trees can have awareness which can also extend beyond their physical bodies.
As such, they obviously exist - but their exact definition and nature is quite hard to grasp. I don’t think they can survive physical death.