To my laymen brain this seems very similar to Lee Cronin's Assembly theory. Curious to understand more about the difference.
Assembly theory is a theory that tells us that when we observe the complexity of something that is not unoque, we can determine probabilistically from it's complexity the likelihood of it being created by some type of active agent, mind or something. Lee continues with this to speculate a lot more (and I think he's on to something) about time being fundamental and what a mind is. It's sort of a computational complexity theory applied to intelligence.
This "phase transition" hypothesis is basically saying that life is emerging in the universe in a stage akin to recombination[0] as a more stable state, and that the universe without life is a metastable state[1]. This would mean that life will ultimately absorb all matter in the universe, as if it were a phase transition the cosmological principle says that the universe is uniform[2].
It sounds like a pretty idea but I'm not really convinced, phase transitions propagate at the speed of light. An exponential curve where the transition ramps up is am interesting idea to ponder. There are existing fantastic explanations for life that exist that are very interesting that don't require the universe to undergo a phase transition. Simple entropy and the red shifting of energy explain it's existence just fine. Nevertheless, all this research and these attempts to understand what life, consciousness, minds, creative agents and all that are in the context of our universe are really fun and I think all this exploration will bear some delicious fruit.
[0] https://en.m.wikipedia.org/wiki/Recombination_(cosmology)