New proof dramatically compresses space needed for computation

We can evaluate various courses of action, and pick one based on that evaluation. I think something like that is what most people think of as having free will. If we discover that evaluation function is deterministic, it shouldn't change our attitudes to it imo. This is how we normally think of the past: what we did in the past is now determined, and yet we were just as free then as we are in the present. And we presently either suffer or enjoy the consequences of those past decisions, so we better take our present decisions reasonably seriously.

In general I'm quite sceptical of taking physical theories as guidance for life, even more so speculative interpretations of physical theories. Physics can tell us, probabilistically, how relatively simple systems will evolve in time, but most events in our life are way beyond what it can predict, so that should caution us against extrapolating its concepts to these more complicated phenomena. We don't know what conceptual innovations might be required to have a fully coherent and precise account of them, or if that is even possible. The best insight we can get on our life is to acutally live it and reflect on those experiences.

Other considerations are that we don't currently have a fundamental physical theory, since general relativity and the standard model don't work together. Even when they do apply, the equations can't be solved exactly for systems of more than two particles. Everything else involves approximations and simplifications, and in fact even the concept of particle is only valid in a non-relativistic approximation. That suggests to me that physical theories are best thought of at the moment as tools that have a limited domain of effectiveness, though of course within that domain they're extremely effective.