I updated the post with the class list so each power source has three classes. It works out reasonably well. The five power sources either derive from the impersonal properties of the Weave (Arcane and Divine), or else the personal properties of ones own Soul (Psionic and Primal, even Martial).
The Martial classes rely on the innate lifeforce of the body, the aura, the self, the body soul. This helps explain some of the superhuman class features, especially at the highest class levels. The Psionic power source is ones own soul, relating to consciousness, presence, and influence. Its psychometabolism sometimes manipulates the body as well, especially for shapeshifting and healing. This is achieved by mentally visualizing a new self, and the body shifting into these mind forces. Psionics can alter the body, but Martial lives the body to its fullest.
This Psionic Barbarian is mind over body. The Berserker is psychometabolic, applying the fury of altered states of consciousness to combat. Likewise the Beast becomes the soul of an animal. The Zealot is dedicating ones soul wholeheartedly. The Tree includes aspects of Primal plant and Divine structure, but is ones own soul as a microcosm of the multiversal macrocosm.
The sourcing for Warlock and Sorcerer might surprise. Generally speaking the earlier class traditions made the Wizard−Sorcerer−Warlock continuum too difficult to distinguish why Sorcerer and Wizard were not the same class, or why Sorcerer and Warlock were not the same class. To assign different power sources helps separate these classes from each other. But because of the earlier ambiguity, various power sources can make sense. So to explain why one power source and not an other, is a choice.
I would have made the Warlock the Divine power source, focusing on religiously forbidden magic, a kind of anticleric. Its patron features can parallel the Cleric patrons. The main reason I decided against a Divine Warlock is because I feel too much of Warlock flavor is the Fey patron. Removing Fey flavor from the Warlock somehow makes it feel less of a "witch". So I left the Warlock as Arcane. Arcane itself has overt flavor, namely science (protoscience). This Arcane flavor strongly emphasizes the Material Plane and its laws of physics and chemical constitution. In this context, these entities that the Warlock class bonds with, know something about the Material Plane and how to manipulate it. The Warlock patrons are doing science, albeit by means of secret knowledge often hostile. Sometimes the more bookish options have the Warlock study these protosciences. But what is mainly happening takes place at level 3 during the "pact". The Patron utilizes Arcane magic to transmogrify the body and spirit of the Warlock. The Warlock character is the result of a protoscientific experiment, sometimes an accident, or a carefully guarded secret formula that Patron only applies to the most loyal supporters, or at least the supporters hoped to be loyal. Ultimately, Warlock magic is Charisma, because it is self-expression, even if the pact has fundamentally altered the "self" of the Warlock. The Warlock becomes the piece of Arcane magitech technology. Sometimes, the Charisma also applies to cajoling future magical favors from the Patron.
Perhaps surprisingly, the Sorcerer is Divine. The sorcery is too innate, too nonintellectual, to match the protoscience flavor of Arcane magic. And here the Warlock pact already covers the flavor of protoscientific enhancement. Perhaps it relates to Primal, but clearly, the Sorcerer embodies planar magic, and here in this setting, is especially Astral magic. The core subclasses of the Sorcerer are Clockwork (≈ LN plane Mechanus), Wild (≈ CN plane Limbo), Aberrant (≈ antiastral Farrealm), and Draconic (≈ Astral dragons involved in the formation of the Material Plane, including Bahamut, Tiamat, and the Ruby Dragon). There can be other explanations for the subclass features besides these go-tos. The main idea is, the Sorcerer is a living portal of an other level of being. The character is a multiversal anomally, and ones magical phenomena are normally evident at birth. Notably, at least for this setting, there are no Fey or Undead Sorcerers, albeit there might be Sorcerers warping the planar fabric of Arvandor or Hades, respectively. The Astral Sorcerer is living poetry, the resonating songs of a particular plane of existence.
The Cleric utilizes symbols and prayers. The Paladin utilizes oaths and exhortations. Both are aspects of linguistic communities. Divine magic is language itself as a fundament of reality. It is the Word, the Song, the Vibration, the Structure, the Organization, the Reality. Divine magic always involves speakers of a language. The Astral Plane is the stuff of language, where archetypes, paradigms, ideals, concepts, and cultures exist independently from matter. The Elemental Chaos is the threshold between the Astral Plane and the Ethereal Plane, where Astral concepts begin the process of emanating ethereal forces, erupting at first like a steady-state Big Bang.
Druid, Ranger, even Monk are Primal. Primal magic is the features of nature existing as a kind of person. The Primal mages form personal relationships with these features of nature. The mountain is a person of earth who likes to relax and enjoy existing. Sometimes, a mountain wants something different. There are essentially six elements. Ethereal force is physical but immaterial. Gravity and telekinesis are features of ether. The four elements of matter are solid earth, liquid water, gaseous air, and fiery plasma. Mainly this fire is skyey, such as lightning and the radiant sun, but it extends to the glowing hot gases of candle flames and bonfires. Finally, plant is a kind of living element, where the integrating forces and matters entangle life. All three Primal mages involve elemental magic.
Even the Monk has subclasses correlating with Elements, Shadow (ether and plasma), Hand (becoming hard as stone, fluid as water), and Mercy (the living properties of plant). The 2024 Monk seems to be going for Martial flavor, such as switching from "ki" points to more neutral "focus" points. The Primal Monk emphasizes the living aspects of nature itself.
The Wizard and Warlock are Arcane protoscience, roughly the maker and the made, respectively. Where the Artificer emphasizes alchemy, it obviously is protoscience. The Artificer is a pet class. I prefer there to be a subclass where this pet is instead a suit of magical armor. As such, I want this Armor Artificer subclass to be the missing "Arcane Paladin" sotospeak to doubledown on the Wizard-Fighter gish flavor.