fungi are like bacteria, they don't really change in shape. Remember that what we see is basically a limb that drops a bunch of babies, the actual fungi are just filaments in the dirt.

the only differently shaped fungus i can think of is lichen, which is a compound organism made of a fungus body with algae or cyanobacteria inside it.
So i guess that's the most sensible thing for them to evolve into, more complex compound organisms. They already parasitize and control stuff like ants so it's not that far-fetched to imagine them being part of the full lifespan, and hypothetically this could happen to all animals to the point that it's as normal as animals having mitochondria (which are separate organisms that were absorbed by our single-celled ancestors).

Imagine that, having a fungus that's just utterly interlaced through your body, like a secondary nervous system and extra layer to the immune system!