Not sure as to the mushroom identity, but when I've seen this happening with potted plants, it's usually due to the soil being too damp and needing to dry out more between waterings. The consensus on the houseplant side is that the fungus itself isn't bad, and neither is the mushroom itself really, but that seeing shrooms isn't common and probably triggered by wetness
I think it’s nothing particularly weird, I’ve always assumed that there are spores in the soil and it happens when it gets a bit too much water, no? I don’t think they need to worry :)