I can't recall Tolkien's works being other than vague about how Sauron took over Mordor. I thought it was a spectacular way to transform the Southlands into Udûn (although the Vale of Udûn is farther north). Just don't think too deeply about how such a contrived mechanism could have been prepared.
I think there might be something to the notion that Sauron was split into two entities by Adar, and that this series is bringing Halbrand and Meteor Man together to recreate him. Presumably, they would cast someone new to portray the reformed being who is the fair form of Sauron. He need not be called Annatar or "Lord of Gifts" as that always seemed to be an honorific to me. There's no Southland left, of which Halbrand can be lord, so that plot thread is pretty much terminated. It was just a way for the show to get him closer to Meteor Man. Neither of the two halves seem aware of their destiny other than being drawn toward it, sometimes reluctantly. Halbrand does seem to have awareness of his past as seen with his interaction with Adar, but Adar doesn't recognise him. I'm attracted to this theory but not completely persuaded that it's correct.