Is it not likely Hakari can heal the soul?
It is shown to us through nanami that sorcerers can interact with soul subconsciously. Nanami was able to guard idle transfiguration from Mahito by just subconsciously guarding his soul with ce reinforcement and Hakari who scales massively above him in jackpot that has unlimited/infinite ce pouring from every inch of his body (including his soul) should be able to do the same.
The reason why this leads me to believe that Hakari can heal the soul is because of the way he heals in jackpot in the first place. Hakari has infinite ce so when he gets hurt his body reflexively heals it due to the overwhelming ce in his body causing the place that is damaged to reflexively heal even though he doesn’t know how to use rct and doesn’t know how to target certain damaged body parts in order to heal it. We see this with even more complex ways of healing when Hakari healed poison even though you have to consciously target that poison in order to heal it but his infinite ce targeted it for him while he was unconscious.
Meaning if Hakari’s soul got damaged the infinite/unlimited ce applied to that soul should reflexively heal because of the overwhelming ce applied to it. People treat soul healing as if it’s not as simple as targeting the soul and healing it like any other way you would heal. It’s just that majority of sorcerers can’t interact with their soul making it extremely rare.
Hakari’s rct is automatic and he doesn’t have to perceive things in order to heal so I don’t know why it’s a hot take to say that he can heal the soul as well without being able to consciously perceive it.