The photosynthesis is actually a retcon, and a pointless one at that. In the original manual the protoss were stated to be hunter-gatherers in ancient times, now their units rely on pylons for power (presumably including nutrition since it serves the same purpose as Terran supply, which includes both ammo and food).
Fungi are neither plants nor animals nor a blend of the two. They are more closely related to animals than to plants. Fungi are heterotrophs, like animals, that decompose organic material for sustenance. They are reliant on plants to survive, like animals. Lichens are fungi which host colonies of symbiotic algae to make themselves autotrophs.
Fungi do not make sense as being midway between photosynthesis and self-modification. That is a non-sequitur.
In fact, the zerg creep is in all likelihood photosynthetic since it serves as the source of all zerg nutrition.