I searched a bit . their souls are definitely immortal. Ill also put some more info from the wiki of Emet
https://finalfantasy.fandom.com/wiki/Solus_zos_Galvus :
He remains convinced of the importance of the balance between Light and Dark and considers his people the definition of perfection while viewing the "broken" races mere imperfect parodies of his kin. He extends this contempt to his mortal grandson, Varis, having no real interest in the Empire outside its intended purpose of spreading chaos. His resentment towards Varis also stems from him resembling his firstborn son, whose death serves as a final reminder of mortal imperfection in Emet-Selch's eyes. However, he does show interest in certain mortals who underwent the Umbral Calamity numerous times.
Also inside it says they didnt rewrite the laws of nature ill copy from the wiki again :
Falling into despair when seeing their world besieged by a calamity from within, he joined his fellow Convocation members and devised a plan to halt the calamity: summon the will of the planet, the primal Zodiark. The price to accomplish this feat of summoning would be grave, and caused one member to leave in dissent. Half of their people were sacrificed to offer up the necessary aether to complete the ritual.The deity succeeded in its primary purpose, but then enthralled Hades and the others into becoming his devout followers. The Convocation resolved to sacrifice another half of their people to replenish their ruined world. Next, for Hades and the Convocation to restore the lives of those originally sacrificed, Zodiark would require even more aether; aether that would come from the new life being born into the world.
This disturbed the dissenting member of the Convocation, who felt that the sacrificial costs were already too great, and that the world now belonged to the lives birthed in it. An opposing group of Amaurotians who felt similarly thus summoned Hydaelyn in opposition to Zodiark, and the resulting conflict ended with Hydaelyn's final attack shattering reality, sundering the world and nearly all life on it into the Source and its thirteen shards.
Ill try to search a bit more though im quite certain they indeed were immortal since like the wiki says he views death as an imperfection