Is cordyceps a mushroom or a fungal plant, and how is it formed?

We all know that cordyceps is a very precious Chinese herbal medicine, so is cordyceps a mushroom? Is cordyceps a fungal plant? Or is it an animal? The claim that it is an animal is incorrect; it is a plant, and as for whether it is a fungal plant, just look at the introduction below.

 Mushrooms belong to the fungi and are rich in amino acids; cordyceps is a complex formed by a fungus parasitizing the young eggs of some insects,growing in the body of the larvae of the moth of the order Lepidoptera, the bat moth,a Chinese herbal medicine. Cordyceps belongs to the family Clavicipitaceae, a complex of the stroma of the fungus cordyceps parasitizing the larvae of insects of the family Hepialidae together with the larval cadaver. Cordyceps is afungus of the family Clavicipitaceae.

Its growth process goes through: the bat moth lays eggs >> the larvae develop and grow >> the larvae are infected by the cordyceps fungus >> the cordyceps fungus fully infects the bat moth larvae >> the cordyceps fungus grows and disperses fungal spores, a complex cycle of steps.