Psychic Powers: Of course, there is absolutely no such thing as psychic powers.  Don’t exist.  No place in a rationally organized universe, like any relatively firm-to-hard SF universe.  Can’t seriously believe otherwise.

But that said…

Telepathy/Empathy: Do you believe in wireless networking?  Evidently the Precursors did, and they really hated waiting while runners were sent or shouting was done, because they built this one right in to the brains of their favored manufactured race.  If you want to detect telepathy, you’ll find it in those weird screebly neural-gestalt signals hanging about in the high microwave part of the EM spectrum.

Precognition: Do you believe in clionomy?  (On the large scale, the gentle art of computing statistical predictions concerning the future of organizations and societies.)  And very advanced predictive algorithms?  (Because with a computer in your head and advanced enough body-reading, simulation and prediction software – and maybe a little SQUID use – you can read people and predict their future actions in a downright spooky manner.  Especially when done in combat.)

Psychokinesis: Do you believe in implanted vector-control effectors?  Another fun now-reverse-engineered Precursor leftover tech, these tiny nervous-system-integrated nanopicosomes are all you need to toss gravomagnetics around, fetch yourself drinks without standing up, indulge in wuxia wire-fu, and kill people with your brain to your heart’s content.

All available in stores for the usual enhancement prices, should you be unlucky enough not to be born with them built in…