It is interesting to see how these spin-offs interpret Hades' defeat as only losing his body in battle, this indicates that Athena never affects or destroys his soul in any way during the fight, and only destroys his body.
In Rerise of Poseidon, Hades clearly mentions that he lost his mythological body, his army of evil/demonic stars and his kingdom built with care by him, it is never mentioned in any way that his soul was damaged in any way, that is why we see the god communicating with Poseidon through a Fairy of the Underworld before disappearing, in short this is similar to Aiolos talking to Aiolia through his armor. So in this story it is clarified that Athena does not destroy or damage the soul of the god, curious because even Ikki in the original was going to destroy the soul of this god, perhaps they used the excuse of Athena's goodness and that is why she did not destroy the soul of this god or simply these authors consider that Athena cannot destroy souls.
This is also mentioned in the description of Saint Seiya Tencent, where it is said that Athena's attack only destroys Hades' body and this caused his soul to fall into an eternal sleep. Although in this story it seems that the Underworld was not completely destroyed and only the structures of this place were destroyed.
It seems that these stories and the writers consider the immortality of the gods to be less impressive even than expected and if you destroy his body, the god is basically defeated and will not be able to return by conventional means, although eventually if the situation arises or he receives outside help he may return, basically an immortality completely useless for combat.
If Kurumada follows this concept, although it is unlikely, or if Rerise of Poseidon is canon (because, well, the videogame is not canon in any way), because we know nothing about it, it indicates that the immortality of the gods is ridiculous, because they have no level of regeneration, they can basically die from insignificant damage to their bodies, and the fact that they can exist as a soul is something completely useless, since they are as useless as mortals in this form, because they cannot possess any body (only a destined human) and cannot interact freely with the world.
Although well, in Rerise of Poseidon it is also mentioned again that Hades created the Underworld and it is literally said that the Underworld disappeared completely after his defeat in this battle, it is even said that the Saints are currently floating in a place without heaven or earth, and we basically see an empty space, something similar to the space left when Zeno destroyed the universes in Dragon Ball Super.
This also indicates that Athena's barriers withstood the destruction of this place, previously I believed they had escaped the destruction of this place, so Athena proves once again why she is the superior goddess in this, even Hades believed she was going to die in the destruction of this place, but she not only survives but also protects the five Bronze Saints.