look I am sad that psionics in 1phb is not possible but I take great effort to not get my hopes up anymore.
I knew it would not happen and hoping for it like hoping for anything is a waste of time.
I can think of four realistic ways that they might implement psionics.
a. a bonus set of abilities to a small number of characters (as in AD&D).
b. a class, with subclasses that allow you to specialize in different niches (this was presented in UA in 2015 and 2016 as the Mystic)
c. psionic subclasses for a select number of existing classes (this was presented in UA in 2019 and 2020, and then implemented in Tasha's).
d. feats
(Currently, 5e uses both c. and d.)
a. is fundamentally imbalancing, and won't happen.
b. was met with strong negative reaction, and abandoned. I think that's a shame, since it is the model that is most robust, providing a psionic chassis and allowing a wide range of expressions. It allows for a class to have spellpoints, which many like, and can give a distinct experience of play.
c. allows each existing class (eventually) to have a subclass, and -- if Tasha's is backward compatible as many hope -- it's already "official". The fact that you are raising the question, though, suggests this is not meeting your desires.
d. tasha's also introduced some psionic feats. These weren't playtested, so far as I rmeember, but they're clean, and even though it leads to a blended approach, they are powerful feats, and so have been met with approval.
It appears (to me, without access to the data) that the fanbase is pretty well split between b and c. Neither option is going to meet with wide approval, but the response when they playtested c. was less negative than b. (There is also a substantial group who have their own private implementations, but
All that's to say, many want psionics, but there has not been a strong rallying around any specific implemntation. They went with the least unpopular, and it offers clear rom for growth (as other classes also get subclasses that are in some sense psionic), and they also offered a few psionic feats to get more buy-in.