Atman does not literally mean soul, self, as we use it in English. But it means self-valuing, i.e. the process that perpetuates itself through breath (breathing is valuing oxygen).
It is not an “atom” in the sense of solid object.
But Atman is the individual self-valuing.
I.e. that principle that has become the heart of the being of flesh and blood but is still the principle.
From Experience I know what Atman is. Such truths are only comprehensible through practice.
It should speak for itself as these religions aren’t fundamentally theories but Methods. At least when approached right.
The difference as outlined by wiki:
" in the Vedanta school of Hinduism, Ātman is the first principle, the true self of an individual beyond identification with phenomena, the essence of an individual. "
“Anātman, a creation of Brahman which is non-different from Brahman and has no existence apart from Brahman.[5] To comprehend the difference between ātman and anātman is to become liberated.”
What is indicated is the difference between the individual working-principle and the universal abstract-principle.
Brahman is the original ground, i.e. the necessity itself that gives rise to the infinite extensions of itself, i.e. all the instances of the working principle.
To become united with the universal principle is to transcend the identification with the particular working principle Atman (which itself was already a form of illumination compared to the belief in a soul-atom, which is the profane and hollow notion of Atman held by the uninitiated), and thus liberate oneself from the wheel of rebirth.
Consequently, one may choose to appear under the limiting laws of the working principle (i.e. as a manifestation of self-valuing logic) in order to represent it in its pure form, i.e. as an extension of its ground which is necessity, i.e. Brahman.
So, continuing on the OP, the Atman requires the self-perpetuating illusion of “self”, but it is not itself the illusion. Once the Atman sheds this illusion through illumination, which is to say, destroys itself in the blaze of its own power (the white void) it realizes Anatman, and basically becomes a value-ontologist.
The current form of Odin is in this sense the the ninth Bodhisattva. These times will not find their liberation in Dionysian Anatmanism, but in the Runes, which are the paths of liberated being.
I do not presume to be understood by dogmatists. I would take offence, in fact, if they pretended to.