Jellyfish eat animals and animal byproducts, so no, they are not vegan.
Jokes aside, often vegans follow dietary restrictions for reasons other than an ethical or moral belief against causing pain. Many vegans don't even eat honey, so I imagine jellyfish is pretty safely in non-vegan territory.
Nothing is 100% vegan. Animals have existed on this planet for hundreds of millions of years, and they are a part of its composition. Soil is just fully decomposed plants and animals. No matter how vegan you want to be, you can't escape eating something that has fed on animal parts directly or indirectly.
If no, what about coprophagic mushrooms (I'm not aware of any fungi that are both edible and coprophagic and also produce fruiting bodies aka mushrooms big enough to possibly harvest)?
I thought your first sentence was serious at first, since it genuinely makes sense to me. If growing a jellyfish causes animal suffering, I can see why a vegan may reject to eat it for ethical reasons.
My mother has a hive in the garden. The bees pollinate our garden, live lives as nice as bee's lives can be and, at the end of the year, we take some of their honey and replace it with sugar, which the bees don't care about.
It's a win-win, nobody is hurt, nobody is taken advatage of.
1 - It's the backyard chicken problem. Yes your mom doesn't harm them, but when producing at scale people care less about not harming them
2 - Replacing their honey with sugar is not good because it lacks the vitamins and nutrients that honey has. It's very possible that you don't take all the honey so they are never harmed by the actions, but when farming at scale people will absolutely push the limit.