Wherever there is matter in an ever-thinning universe, there might be an entire cosmologically-sized era dominated by an entirely different chemistry to what we have now.
This is just what Big Boson wants you to think.
No because that state refers to bosons only.
Once the universe has expanded sufficiently, there will be no more reactions at all. Protons and electrons will be too far apart to interact. There maybe a few remnant pairs of neutrons and protons, but eventually even those will separate to distances where they won’t interact.
You’re right about bosons, but there’s another reason BECs won’t dominate. BECs require extremely high density along with near-zero temperatures. As the universe expands, particle density drops dramaticaly, making the conditions for quantum condensation impossible to achieve naturally. The distances between particles will be so vast that quantum effects requiring proximity (like BECs) simply can’t form.