So I like the design behind psychic dice a lot, particularly as an alternative to spell slots, but there's 2 points that are standing out as kind of weird tensions to me. First, the heritage options that add extra psychic dice seem to work great when you're mixing them in for some mild psionic flavor, but do weird things to the Esper's progression when you take them alongside the class. Extra dice as a mild resource push feels okay, but gaining access to the 3rd tier effects of powers 2 levels earlier than someone without that heritage feels off.
And then the second point, I'm not totally sure I get the design intent behind the Thymokineticist's Unfettered state. If I'm reading it correctly, you still have access to all your psychic dice, but you can't lose or gain them? That feels like it violates the primary design constraint on a lot of powers and really pushes the game toward a lot of encounters/day without short rests, to burn through the Esper's dice, and at higher levels unless the Esper is regularly risking them on utility powers between fights, they just won't be constrained on dice in combat, because of the recharge after losing 2 dice.
Disadvantage on Wisdom saves is definitely not nothing, but I keep looking for some downside intrinsic to the ability, that isn't just a vulnerability for enemies to capitalize on. It feels standout better than what the other archetypes can do with that slot.
So for the Heritages and Progression:
Progression is kind of a strong term for what happens with the powers of an Esper. Warging is not significantly more powerful at level 1 than Telekinesis is, when you break it down. As it is, a Chirurgeon, Medium, or Thymokineticist could begin play with 3 disciplines in their chosen power and the power granted by their archetype. It doesn't make them particularly stronger than a Psychic Warrior, who gets more options through the Awakened Mind, or the Mindhammer, who gets two attack additional options for their bonus-action mind strike.
Just more flexible in their power choice moving forward.
And that is, really, the Esper's core identity when it comes to being a "Caster". Narrower and more defined ability, wider flexibility.
As far as the Unfettered state.
It is pretty powerful at retaining psi dice, yes. But it also locks you out of recovering psi dice. And if you use it early in the day while you have max dice, you can't use it later when you might need it. And later, you might have limited dice availability and really need that 6 you rolled to recover a Psi Dice. So it's very much going to be a balancing act of this particularly potent resource.
There is another consideration worth noting. You can use the Unfettered State when you have no Psi Dice available. Which means it can be used in a purely defensive capacity when you're otherwise wiped out, providing resistance and Temp HP to keep you standing, as well as -some- protection against long-lasting Wisdom-Save induced effects.
Though it does kinda throw me for a loop that in the Psionics section in the Esper class seems to dictate that Augments are to be selected before taking the Manifest action, but the language in some powers, such as the Astral Body power, seems to indicate that the augments can be used after Manifestations
Specific beats general. Some powers, like Astral Projection and Warging, allow you to change how you're spending your augments on their continuing effects, essentially. Such powers are providing round to round changes and options that require a secondary investment of Psi Dice.