Within the Avatarverse, there are different levels of self that are important to distinguish in order to understand the concept of spirits and reincarnation cycle.
A soul is a being’s existential core, the unit that’s tied to life and the cycle of reincarnation. When Korra used spiritbending on UnaVaatu, she destroyed Unalaq’s soul, removing him from the reincarnation cycle for all time. A spirit is an individual’s very essence, a part that’s unique to themselves and can be sent to the Spirit World. Avatars are able to connect their spirit with the spirits of their past lives by using Raava as a conduit. Think of it as a single flame lighting multiple candles; the spirit is each individual fire, while the soul is fire itself. The flame on each candle is the same as every other fire, yet still separate and unique.
Iroh didn’t enter the Spirit World in the same way those stuck in the Fog of Lost Souls did; rather, he essentially reached the Avatar equivalent of Nirvana, becoming an enlightened being who transferred his essence into a spiritual form. The Painted Lady was another individual to achieve enlightenment, and she became a bodhisattva-esque figure for the village she watched over in life. Compare this to Avatar Kuruk, who entered the Spirit World to find Umi and defeat Koh, and supposedly stayed there for centuries even as the Avatar Cycle continued as usual.
The implication is that the Avatar cannot reach enlightenment, because their duty to the world means they must remain tied to the cycle of reincarnation. Yangchen has stated the Avatar has to give up their spiritual needs for the needs of the people they serve; they ultimately must remain attached to life, humanity, existence. This is both a noble sacrifice and a curse, depending on your point of view.
I don’t think you’re too far off about the meaning of the void. Buddhist concepts of “the void" (śūnyatā) hold it to be a meditative and philosophical view of detachment from existence. Quotes from Guru Laghima that Zaheer has dropped throughout the season reflect many of the ideas inherent to this concept. “Instinct is a lie, told by a fearful body hoping to be wrong,” is the recognition of a non-objective existence and reality; “let go your earthly tether, enter the void, empty, and become wind,” speaks of a state of spiritual detachment and separation from meaning; “new growth cannot exist without first the destruction of the old,” once more implies an ever-changing existence of both positives and negatives.
Voidness is often mistaken for a form of nihilism; I might be recalling this wrong, but I believe Nietzsche has been referred to as the European Buddha for this very reason. This, however, is a misread of the philosophy; nihilism draws from the idea nothing has meaning, while voidness states that meaning is entirely relative. Bobbityhobbity has written a fan-freaking-tastic post about Zaheer’s apparent adherence to nihilism, and I think this is generally consistent with what we know about Zaheer’s philosophies. He takes elements of Guru Laghima’s teachings and discards many of their applications in airbender life, revering traditional airbending as an art form yet disregarding the Air Nomad’s vow to pacifism.