Psionics is just Space Magic by another name. No need for a new system.
I would say that the problem is that even if psionics are "space magic," how 'magic' operates or functions is incredibly broad, particularly within the realm of fantasy itself: e.g., spell books, spells, rituals, material components, incantations, at-will talents, etc.
For example, Blue Rose has psychic arcana as a type of magic that operates like other magic in the setting. However, other magic in the setting involves at-will magic, often requiring Adept characters making rolls against fatigue. Magic does not involve spells cast from spellbooks, using spell slots, or spells per day.
This is one of the chief problems with the discussion about whether or not psionics are "magic." Even if one agrees that psionics are a form of magic or magic by another name, one does not necessarily agree that psionics should use the spell level/slot system or that one should use wizards and sorcerers instead. But that is often what happens in these discussions: i.e., a LOT of bad faith bait-and-switching.
To me, "Star Wars" force abilities don't frame very well as psionic abilities. They do have power crystals (in light sabers, and in certain powerful weapons), and The Emperor uses technology to boost his abilities. (I'm discounting most of the new abilities in the last trilogy. I can't fit them into my prior conception of the force.) But the Emperor seems to use technology more to facilitate his force use than to actually generate force effects. To me, the force just doesn't feel psionic.
There seems to be more overlap between the Force and D&D psionics than with the Force and D&D magic (
on the whole). The Force is in many respects like Ki, but Ki and Psionics have been linked before in D&D (e.g., 4e D&D). But the Force does involve meditation, telepathy and empathy, telekinesis, mind-over-matter bodily enhancement, heightened reflexes, intuition, lightning powers, precognitive visions, psychometry, mysticism, etc. which are common powers, including in terms of flavor text with D&D psionics. It's hard to imagine that D&D psionics weren't likely influenced by the Force, Jedi, and Sith from Star Wars.
Psionics sort of suffers in that it has migrated from something that may have seemed somewhat plausible as something that might exist at some point in the future if you squint your eye and don't study the science to closely.
If people have some small degree of psychic ability, which was actually something being seriously studied at one point, then it would make sense that genetic manipulation or eugenics might one day enhance this ability.
I don't think people take this seriously any more. It's sort of slipped now into the same realm of magic in most people's imagination. However, it's still viewed differently to how magic is usually viewed, because it's origins in a form of pseuo-scientific thinking inform it's use in genre.
As I said earlier, think about whether psionic powers should be able to animate zombies and have them walk about of their own volition. Necromancy assumes that death is a kind of energy of it's own that can manipulate things. Psionics (generally) assumes that the laws of phyiscs roughly apply (except where they can be broken in the expectation the average person won't notice)* and that you can't use mysterious metaphyical forces like the power of death.
There's also degrees of proximity. Once you have a hard science fiction in space in which people have a limited form of psychic ability, the the more pulp arm of the genre which take that and stretch it past the limit of plausibility, because you are allowed to do that with the pulpy arm of the genre. It's the more fantastical element but it exists in a kind of dialogue with the more serious.
Psionics, IMHO, represent - much like 19th century Spiritualism - a reaction to the scientific materialism, reason, and empiricism of Post-Enlightenment worldview. It represents a desire for a continued place of the magical, otherworldly, miraculous, and paranormal elements that were previously a part of (predominately) Euro-American worldviews.
Considering how many people still treat wizards as the scientists and academics in a world of magical fantasy, I'm not surprised (in retrospect) of the continued desire for psionics.
the problem is the mutant fantasy has been more or less eaten by the sorcerer so going for the universalism of the spiritual seem the best bet but that means we would have a whole bunch of new problems to deal with.
I think that there would have been far less of an issue had D&D 5e gone the PF2 route and came up with four universal spell lists: i.e., Arcane, Divine, Occult/Psionic, and Primal. So if you want your mutant fantasy that you were born with psionic powers, pick the Occult spell list. Is your in-born gift that you were born with powers of nature and the wild? Pick the Primal spell list. That would have also been a great way to provide a place for psionics at the start.