I know... old thread. But I think it's an important topic seeing as the plot of BG3 starts off on a Mind Flayer ship. So some sort of Psionist class of some sort would defiantly belong in this game. And I am not talking a weak toned down subclass as WotC is proposing, but a true focused class based on mental powers. And though I am unfamiliar with the "Mystic" class as it's been a long time since I last played the pen and paper variants of the game.
You see I have a little different perspective as I stopped playing at AD&D 2nd edition back when TSR still owned it, and I never really cared for how WotC changed things when I looked at picking things back up again after 2000 3rd edition. As their view of the game was different from how I saw it. But I always loved psionics, and especially loved the world of Athas (Now that would be a super cool game for Larian to make). But to achieve that... a real comprehensive Psionic system would need to be put into place as well as a class dedicated to that. I just think it would also add to this game, especially with how the introduction plays out.
Not going to happen. This is a licensed D&D 5e game with tons of source material to implement. Besides, going completely off-script would cause an uproar in the community who indubitably have their own favorites from the various official books.
I would suggest you consider playing a Githyanki Great Old One Warlock. The subclass is still not properly implemented, but you should get plenty of racial and class powers and spells that are psionic themed. You would get telekinesis (ie. Mage Hand), telepathy/mind influence (ie. Charm Person), pyrokinesis (ie. Fireball), cryokinesis (ie. Ray of Frost). Those spells not specifically of psionic origin can be roleplayed as such. If you want a more martial psionicist, consider Eldritch Knight. A more stealthy psionicist, pick Arcane Trickster. Then pick appropriate spells.
Outside this, you have increasing powers from the illithid tadpole which are psionic in nature.
