Well, first of all, there is no canon. So if you want to play around with psychic abilities, go for it.
That being said, a lot of the "psychic stuff in the staff" stuff is written in terms of passive things. Psychic resistance, ability to receive telepathy, that sort of thing. Anything active would certainly be an SCP. Generally speaking, the staff of the SCP or baseline humans, with no inherently different capabilities than humans in the real world.
Yes, there are in-universe senior staff with… oddnesses (Bright, Kain, Clef, etc.), but keep in mind that most of them were established back when the site started and are NOT to be emulated nowadays. If their characters had never existed and they tried to introduce them today, they'd get shot down.