The easy answer is to put them in the boxes.Here is my thoughts.
"Magic" manifests in a variety of mechanical ways: spells are the most common but you see things like class features (channel divinity, wild shape, invocations) that are also "magic" but not spells.
D&D used terms like Arcane, Divine, Primal, etc to describe how these effects originate, but they are 100% fluff and have no mechanical weight. Further, they aren't intrinsic to the class itself, as a subclass like the divine soul sorcerer reflavors the normally arcane sorcerer into a divine class.
Psionics is just another flavor description like Arcane or Divine; a way to describe why an ability functions. It can be a "spell" or it can be a class ability (such as the soul knife's psi-blades). And That works just fine in 99% of all D&D settings because it doesn't matter where the"magic" comes from as long as it's effect is balanced.
Except in Dark Sun. Dark Sun cares too much about where it comes from. Dark Sun wants to ban divine, corrupt arcane, limit primal and others and exalt psionics. Which doesn't work with 5e because there is no link between these terms and how the game handles magic.
To whit: most people would argue a sorcerer is an arcane class. It fits the aesthetic and has been described as such. In a Dark Sun game, it would be subjected to the defiling rules (if it were allowed at all, purists are a fickle group). However, not all sorcerers are Arcane. Divine Soul sorcerers are divine powered. Aberrant Mind sorcerers are Psionic. Arguments can be made about Shadow sorcerers using shadow magic or storm sorcerers using primal or elemental. If power source matters, every one of those subclasses could be subjected to different rules, despite being 95% the same class.
So the biggest problem is that classes don't neatly fit into power source boxes anymore. That makes designing rules to interact with them tricky if not impossible to future proof.
Even if d&d as a base does not recognize a difference between divine magic and arcane magic for the purposes of mechanics we can still use it in Dark Sun by applying that definition.
Also worth noting in Dark Sun? I would consider divine soul sorcerers to be arcane casters even when they cast spells that come from the cleric spell list.
Because the real definition of divine magic is that it can be taken away. If you don't do what your God wants or you break your oath your power goes away. The divine soul sorcerer has that divine spark inside of himself so that power cannot be taken away.
Also I probably wouldn't allow Divine soul sorcerers in Athas anyway.