Hive Minds in Stellaris are a bit more specific than some settings, they are more a single mind where every drone is an extenstion of its will. Specifically:
"
Hive Minds operate as a single organism more than as a state. The population has no free will, and act as an extension of the Hive Mind itself - much like the limbs of a body.
When cut off from the Mind, these drones become comatose and eventually wither and die. Any free individuals on planets owned by the Mind are driven away, killed, or simply treated as prey to feed the collective."
Psionics could logically form a Gestalt Consciousness, but it would not be the same as a Hive mind, it would be communal psionic link; where individuals are seperate entities that share information and thoughts over a link but remain independently operating individuals. The Protoss from Starcraft and Advent from Sins of a Solar Empire both have that concept. A group mind could be the extreme result, but it would be an ultimate democracy rather than a hive mind.
To an extent you can represent a system like that in game, its why psionics get ethics attraction and there are lots of references to shared thoughts. Maybe at some point it will become an empire type, but Hive Mind does not fit.
With regards to the OP's suggestion: rather than having a new hive mind arise, i think it would be interesting if rebellious Psionics made a pact with a Shroud entity, possibly sacrificing themselves to unleash a massive shroud encursion upon their oppressors. It would fit much better and be very different from the existing robot rebellions.
Given the Shroud is basically a ripoff of the Warp.
The Warp is not an original concept.