There really is absolutely no incoherence in imagining a second universe (or a disconnected piece of this universe, if you prefer), perhaps populated by intelligent beings. I'm stunned that you think this is the least bit paradoxical.
I just don't have anything more to say on this, I suppose. Your pronouncements that existence presupposes interactions (with every single part of that which also exists, I suppose) just comes out of nowhere, near as I can figger.
This is still consistent with the hypothesis that the universe consists of distinct, disconnected partitions, incapable of interacting with one another.
I see that you say this, but I see no reason to think that it is true.
I invite others to weigh in and see which of us has odd intuitions here. It might, I suppose, be me, but I would honestly be surprised.
The universe as a whole exists, but does not interact with anything else, right? Obviously, bits of the universe interact with other bits, but not with anything else.
Now, imagine that the universe has two distinct parts, disconnected and incapable of interacting with one another. The bits in the first part interact with other bits in that part, and the same with the second. If we can agree that the one-part universe exists, then surely there is no reason at all to suppose that this two-part universe is an incoherent concept.
Of course, from the perspective of the people in Part A of the two-part universe, there is no reason to take seriously the possibility that Part B exists, but there is no incoherence in doing so. It would be a perfectly undecidable proposition which has no predictive or explanatory value at all, but it is not an incoherent proposition.
I cannot see any problem with this hypothetical situation.