I agree; even the given origin story basically is like a monk (seeking some sort of perfection), but with tentacles thrown in the mix.
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One idea I personally tossed around last time this came up and thought was kind of interesting is the idea of psionics being old, lost traditions, something more Greco-Roman or Indus Valley or Ancient Mediterranean. This jives with the aberration element (nothin' older than the Elder Things; plenty of lost civilizations paid homage to them), the planar element (immortal, timeless beings), the Dark-Sun-Mutant element (rampant nature evolves these powerful abilities lost to the creatures of this age), the pseudo-science element ("we're discovering ways that the Ancients used their minds that have been lost to us for centuries!"), the Dream World element (the primordial, powerful first dreamings)....
The narrative involves plumbing the ancient depths of ruins and fallen empires long-forgotten to uncover strange and dangerous practices that may have even lead to that destruction (Dark Sun twists this so that the tradition is discovered and known but still held by and elite and might yet bring the fall of today's empires). Strange angels of your far-flung ancestors guide you to lands once tamed by powerful mentalists, now fallen.
The mechanics involve uncovering unseen knowledge, bodily practices that are intense and ritualistic, manipulating minds with a word, even stepping between worlds - things the Ancients could do, lost to all but the most learned of sages today, which you will re-discover. You will also re-discover the dangers that this brought.
The enemies that are most iconic are golems, undead, beasts and oozes and other mindless creatures - they are resilient to your mental commands, they are the things that rule this once-noble land now, memories and savagery.
This narrative is close cousin to the Warlock and the Wizard, but there's not a specific entity involved, and rather than knowledge and lore, it's about practices and transformation.
The subclass themes are about different lost traditions, lost empires, lost kingdoms - you seek out remnants of these lands to learn more about them and the unusual powers they had. And you could have a subclass focused on a particular tradition from a civilization that died from piercing the veil between worlds and letting in things from beyond the stars. Importantly, you could also have a subclass focused on a tradition from a civilization that was a grand eternal peace (imposed via charms and domination) and was lost when the mindless golems overthrew their masters, or a tradition of great and powerful warriors whose control over their body twisted them into monsters (that eventually obliterated the civilization).
In FR, imagine psionic traditions dating from ancient Netheril, or the Calim empire - or any of the other literal "Forgotten Realms."
But that's just one idear.
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I'm quite fond of that little thought experiment!
In my hypothetical narrative above, it would be that the mystic is a student of the Old Ways, long forgotten traditions that once powered great civilizations, and they seek to master them. Perhaps they seek to bring them back and relive the ancient glory days, or maybe they must master these to confront a resurgent threat from long ago, or perhaps a driven curiosity allows them to unlock old traditions abandoned as heretical and dangerous. The powers of the mind are more ancient and foundational than any spellcraft studied today.
In WotC's current narrative it seems that mystics seek self-perfection, because the tentacled horrors from beyond the stars left ripples in the pond of reality that resulted in your abilities.
I would expect that the mechanics based around that would have strong Law/Chaos elements, with the practitioners seeking mastery over a fundamentally wild force. The risk of madness should be real and ever-present, and the mystic would always be looking beyond the next horizon to understand the unusual abilities they've been sadled with. Wild mage mechanics might work OK as a starting point.
The mechanics as they exist suggest a character whose power arises from knowing foundational bits of power that they can enhance - one of them takes it in a "sage" direction, the other in a "warrior" direction. The mystic as a protagonist is a specialist, who has discovered a few tricks and applies them. They either learn how to manipulate others' minds, or they learn how to control their own bodies. This perhaps reflects an outside/inside dichotomy - maybe characters based off of an extrovert/introvert character type. The goal is to discover new psychic powers (this is what they do as they gain levels), which means whatever origin these powers have is something that this character wants to get very intimate with. That these are called "disciplines" points at a character who is fundamentally lawful, imposing their own order on themselves, or those around them.
To help these mechanics match their proposed narrative better would mean more madness, more horror, more "what happens when you push beyond your limits?" elements.
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