For me, I would boil it down to two biggies:
1 - A focus on abilities that are "traditionally associated" (recognizing that this is at least partially my experience/bias of what is traditionally associated) with psionics: Telekinetic effects, Telepathy/Mind Affecting Powers, Personal Body Augmentation, Clairvoyance, and Crystals.
A great side effect of this focus is that characters (especially through sub-classes) tend to be tightly thematically focused. They aren't pulling abilities and powers in random ways and from random sources, it's all tied to a single schtick.
(I'm not completely averse to something like pyromancy or cryomancy or the like, but I'm more inclined to have that concept be a separate Elementalist class.)
2 - Character class mechanical design that leans into the "internal pool of psychic will/strength/stamina", and thus without something like spell slots and spell levels. This could be through a straight up power point pool or instead through augmentable powers (think Monk or Battlemaster -- heck, even Rogues get to augment their powers by trading SA dice for effect). Something akin to how Warlocks mechanically work would also be viable, I think.
(FWIW, I liked the Mystic and it's Disciplines that gained you a base benefit plus a series of preset spells/powers that were augmentable. But as we know that was a bridge too far.)
