Is there actually a lore explanation for why biological machines can get psionics but electronic machines can't? It just seems very arbitrary to me, though I admit it's a common sci-fi trope to treat biologic species as magical in this way.
Random thought: Psionic Megacorp: We're not actually psychic, we just pay shroud entities for their psychic services so we can deduct it on our taxes
Well, to start with, Psionics is the ability to directly interact with the Shroud. We know that it is possible for some machines to do this, and we also know that it is impossible for most machines to do this, from various events.
There is a specific machine paragon that is the Chosen of the Shaper of Clay shroud entity. You can also do it to some extent via Nemesis. But, conversely, the reason the Contingency fails at infiltrating Psionic empires is explicitly because the machine infiltrators it sends do not have a shroud presence.
We can infer from these that
1. Machines, or possibly Gestalts, cannot normally interface with the Shroud (the core of Psionics). This seems to be because they have no souls, and it is probably all machines because empires that are Psionic act like empires that are/become machines have no souls in dialogue. Given they can literally detect something different via Psionics, this is not a dogmatic belief, it is literally true.
2. It is possible to make a machine interact with the Shroud without making it Psionic OR giving it a soul, however as it stands currently this requires either an enormous effort or the Shroud reaching out to a machine, not the machine reaching into the Shroud (as Psionic empires are capable of).
Based on the above, making machines interact with Psionics (within a Psionic empire or Gestalt machines or individualist machines) should be possible... and narratively somewhat exceptional. I wouldn't want to lock Psionic machines behind one specific origin or anything, you should be able to choose to play what you want, but narratively this should be very abnormal. Call the trait Psionic Circuitry, and it can allow machine empires to Psionically ascend while regular empires could use it to for instance give physical bodies to Shroud entities within their own empire.
Hiveminds should also gain Psionic ascension, and all three should be different from each other. The 'primary' version should be for biological empires, but machines and hives should get their own version akin to biological empires getting a Virtuality and Modularity less extreme equivalent with no Nanotech.