I think humidity is a big limiter. 'Mushrooms' are the short lived fruiting body, of the unnoticed fungal body in the soil. Other fungus have interesting shapes that last longer.(google bracket fungus) With that, maybe you choose a glass container or aquarium, and can find some natural outdoor fungus on rotten wood. Bring it in, set it up in your terrarium. I had fresh wood chips spread over my garden which after a year grew a fungus like a bracket kind of fungus that kept growing a long time.
So if you make a terrarium and can hunt for wild fungus on mulch, or rotten natural dead wood, maybe you can foster them for a time.
Disclaimer- Not a fungus expert, but making semi- educated guesses based on garden and nature experience