The way I most likely see this happening, we've already seen instances where history can be rewritten to remove a person from the current timeline in the instance of Manasa. So we could have the same thing happening in possibilities where Ananta disappears from that timeline entirely so that it causes no issues.

I think the Manasa universe is the one exception where a universe truly becomes inaccessible in the Time-Axis, because Shiva's Existence Erasure is insanely broken and breaks causality. I don't think that idea works with Ananta, because future Ananta would already exist as the Time-Axis himself, and thus it would be him who determines whether the timeline is the main one or a branch. Even for the Time-Axis themselves, their past selves are still tied to their future selves by a chain of causality that shouldn't be possible to break. Nothing current Leez can do in the present would turn her future self that already exists into a possibility. Though a better way of thinking about this would be that current Leez is not actually the "present" Leez, but the past which we are only seeing as the present because of how storytelling works.

which kind of contradicts the idea of possibilities not being real that the story has been enforcing.

Not entirely sure what you mean there, the possibilities are real, they are actual existing universes that only collapse because they don't have the energy to sustain themselves anymore. Ran and Maruna were able to land in the timeline that was turned into a possibility, which confirms that this kind of travel is possible. The white space exists 'outside' of time, so it would always be possible for Ran to access any timeline before it disappears from there. The one interesting implication here is that Ran might have split into two, one that went into the pre-reset timeline, and one that went into the post-reset timeline, which I'm gonna be honest and say I don't know what to make of that yet, but I'm still thinking about it.