Still not convinced that it might be fungus. It doesn't look like fungus to me. Escpecially since they do not look like fine hairs and spawn in nice groups. With fungus you would expect a blanket of fungus through the tank.
There are more species of hydra so that's why I thought it might be hydra. However, I do agree that the tentacles might be too short.
So I looked further and found an other possible explanation, namely Vorticella. These are normally harmless creatures, but when they settle with too many in the gills of the fish they might make breathing very hard for the fish.