Precognition and Conceal Thoughts were lower level psionics powers. Sure Conjure Astral Construct could be any summoning spell, much like how Conjure Elemental, Conjure Fey, or Conjure Nature's Ally could be the same, except they're not.
"Mind stuff" is actually a pretty good start, though you may not think so, much as a druid design may be guided by notions of "nature stuff" or a cleric design guided by notions of "god stuff." It gives us a thematic core to work from. So what can psionists do with their minds? They can enhance the mind and senses of either themselves or others (e.g., precognition, telepathy, visions, etc.). They can likewise debuff the mind and senses of others. They can use their mind to enhance their body. They can manipulate objects and/or apply some forms of energy (e.g., force, psychic, astral/ectoplasm, etc.) with their mind. But we are generally dealing with the sort of things that we see psychics, telepaths, telekinetics, mystics, mesmerists, and such in various forms of fiction do.
Reliable telepathy and forming psychic links. Body control. Meditation. Various forms of projection. Empath powers.
One thing that would be worth exploring in the context of 5e would be manipulating with Concentration mechanics. If Concentration represents a mage focusing their mind on maintaining a spell, then how would or could a "mind mage" like a psion relate to it? Can psions concentrate better? Maybe on multiple things? Can psions help others concentrate better? How could psions interfere with the Concentration of their foes? Could they steal spells that others are Concentrating on? Can they gain advantage on actions or abilities when their foes are using Concentration spells?
Maybe psions could temporarily learn/steal spells from their foes that they see cast a spell. Maybe they could cause foes to forget spells that they cast. There's a lot of potential for the psion in being something of an anti-caster caster. And maybe this is why other casters say psions don't do magic or fear psions, because psions can play mind-games with their magical abilities. Clerics view it as blasphemy. Wizards view it as illogical (and "unfair").
Not saying that this is what I want the psion to be, merely brainstorming.
I want a psion, much like a person asking for a cleric should reasonably expect to get a cleric, and I want it to be able to fill its idiomatic class fantasy. If you are concerned about role-filling, then we should be talking about 4e and not 5e.