Instead of trying to create entire new classes, I think it's much more in the spirit of 5th edition to implement psionics with new subclasses. I think I've managed to capture most of the feel of the 3rd edition classes, here, while still fitting into a subclass (2e psionics was a royal mess, and I have no clue what if anything was in 4e for psionics, so I didn't try to match them).

The fact that sorcerers get their origin at 1st level opens up the possibility of an origin that changes their casting stat. And much of the feel of the psion is already present in the sorcerer: Their magic comes from within, not without, they can pull action-economy tricks using Quicken or Twin metamagic, they can expend points to make their spells more powerful, and so on. Adding extra spells known, on top of the sorcerer's base low number, allows the choice of discipline to have a significant impact on the class, but the similarity of many of the spells in each discipline reins in the power increase from gaining so many spells known.

The psychic warrior, meanwhile, is obviously based on the four elements monk as a template. The Soulknife ability is mostly just a ribbon, to enable anyone who wants to convert a soulknife character from 3rd level: It provides very little benefit over just using a physical weapon or unarmed strikes (very few things resist psychic damage, but then, very few things resist the damage from a monk's fists, either). Again, a lot of the iconic abilities are already present on the monk chassis, such as spending resources to make more attacks, or to move more swiftly. The spell (and other ability) list I've chosen is more useful for a martial character than those in the Way of Four Elements, a deliberate decision since I regard Four Elements to be an underpowered option.