>In the same way, if the universe is to actually exist, its properties can’t be exclusively relational/dispositional

People who believe the mathematical universe hypothesis would take issue here (I'm not educated enough to make a full opinion but I know they would oppose this quote). They would say the universe is entirely relational - it's all one set of mathematical relations. Max Tegmark is one such person and he explains consciousness and self awareness as arising out of evolution (being aware and not a slave to sensory inputs can be beneficial), and subjective reality and the flow of time are just subjective/conscious illusions. Albeit he doesn't give a mechanism for consciousness to form in the brain, but no one has yet.

We know literally zero about the natural basis for consciousness -- and I mean zero -- and so that claim (better known as "panpsychism" if you want to research it) is pretty much as plausible as any other at this point. And it's been taken pretty seriously by a great number of scientists and philosophers over the centuries.