Are most Anunnaki psychics female or is gender not really relevant to them in this work? Is this a caste type occupation akin to a kind of priest class?

There are Anunnaki psychics of both genders. Like human, they have had a degradation of capability from long-standing inner corruption by spirit meddlers, but they started from a high level of performance prior to their decline so they can still hold their own quite nicely to do what is needed for their purposes here, despite their spiritual disconnection. Their ability to connect has not disappeared. It is the will to do so.