Fix accurate AD summation in residual equations#1035
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I believe the accurate AD summation types in mesa's residual equations were just being assigned the result of a normal AD expression sum, so the (dp) cancellation had already happened before the compensated summation logic even runs. So the accurate AD summation was not really being leveraged at all. I would call this an inconsequential bug, but fixing it could yield benefits.
This pr fixes the accurate AD sums to accumulate term-by-term through the accurate type, so each add/subtract actually uses the compensation algorithm. I added this type to a couple other locations where it might make sense (summing sources in hydro energy and in RSP2 turbulent energy and luminosity equations), and I did some minor clean up.
I'm not sure if this will help mesa convergence or not, it could in principle, but the point remains: this branch makes the intended behavior on main actually happen in practice. We will have to test and see if any thing changes in practice...