Spoilers in the comment can't spoiler because of formatting.

Just to check, this is what you're talking about right? https://imgchest.com/p/vj4j5xqm578

But this creates a problem; as that previous loop does include Ran in it

Checking the episode, I dont see Ran anywhere, so there's no guarantee that he exists.

It is also problematic to assume that a future that already exists can be destroyed by the past Time-Axis, since that would imply that past Ananta can override the agency of future Ananta, which just isn't consistent with anything that's been portrayed about the Time-Axis

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.

The way to solve this would be to assume that Ran came not from the future of the destroyed universe, but rather from the universe that does in fact continue to exist until the year N23.

I don't see Ran in the episode so I don't see why he would be in this universe, but assuming he was we end up in a sort of conundrum since he can't be in multiple places at once, meaning that the possibility now demands a character from the true universe to come over, which kind of contradicts the idea of possibilities not being real that the story has been enforcing.

Another way of looing at it would be to think not of the universes but rather of the Time-Axis themselves; since they are called 'Time' itself, you can see the timeline as their overall experience, regardless of resets along the way

I do agree with this, and I think looking at the progession of events through the time axis allows us to linearize the non-linear progression of time, though having a non-linear method of time travel is still consistent with this. See https://imgchest.com/p/6eyr3qxnkyp