they seemed to make a distinction here that Setsu went to a different universe which supposedly is totally disconnected to the one we are currently in, and impossible for Setsu to return to and pass on the silver key to past-Yuri.

I had the same thought.

From what I can see right now, the easiest - albeit unsatisfying - way for them to explain away all inconsistencies is that this is all a simulation by Gnos.

It would explain why we don’t see Levi self-destruct DQO when Gnosia wins: that particular universe(?) has ceased to exist / that particular instance of simulation was stopped! (and Yuri looped before we see this)