I prefer the UA approach, implementing psionics via subclasses. I agree with the 5e designers that psionics needs to be a normal part of D&D that players actually use.
Psionic feats are the best way to implement 1e style psionics.
(Additionally, a separate Psion class appeals to me, if it is clearly a full caster with high level abilities like Wish.)
PSIONIC SPELLS
CANTRIPS
Rather, update the cantrips themselves − rewriting them according to the new psionic versions − for anyone to use these cantrips these ways.
Friends: all characters who use the Friends cantrip should do so without incurring hostility.
Message: this should be telepathic for anyone, without pointing or whispering.
Mage Hand: the hand should be invisible for everyone, using a bonus action. However, the weight carried needs to increase while leveling.
TELEKINESIS
Telekinesis remains underdeveloped, and needs to improve incrementally while leveling. For gaming ease, telekinetic abilities should refer to size rather than weight (Tiny, Small, Medium, Large, Huge, Gargantuan). For example, Mage Hand should be able to move a Tiny object or a Tiny willing creature.
PSIONIC SPELLS
Psionic spells effectively gain the psionic tag.
All of the spells on the list are appropriate for psionics: Telepathy, Telekinesis, and Teleportation.
Missing from the list is Wish − which is the ultimate "mind over matter" spell.
Weirdly missing from the list are "psychic" spells, like Augury. At least there needs to be a psychic spell for DM hinting: good, bad, mix, no vibe.
For me, psychometabolism relating to shapeshifting and psychic healing, is an important psionic theme. But it is missing from the psionic spell list. I am unsure how best to handle this shapeshifting mind-over-body theme.
MATERIAL COMPONENTS
I love how 5e allows casters to use a spell focus (like a wand) instead of the material components.
However, for psionic spells, even the wand feels inappropriate. The point of psionics is that ones own mind is the power source. An external object distracts from the direct mind-over-matter flavor. I prefer all material components to be absent, either because of the spellcasting method or the psionic list spells remove it. Also, there needs to be a way to eschew a costly gp component.
PSYCHIC WARRIOR
I like the Psychic Warrior Fighter.
The name has too many syllables. Maybe officially rename the subclass the "Psy" (or Psi). Then we can call it the Psy or the Psy Fighter.
I am satisfied with the subclass.
It would be even better if the Psy can also Telekinese oneself, to levitate and fly.
SOUL KNIFE
I am neutral about the SOUL KNIFE
PSIONICS WIZARD
I like psionics as a Wizard arcane tradition. This is a reasonable way for 5e to represent the 3e Psion of the Expanded Psionic Handbook.
I will discuss this subclass separately.