  We prove that any complete Riemannian manifold with negative part of the
Ricci curvature in a suitable Dynkin class is bi-Lipschitz equivalent to a
finite-dimensional $\mathrm{RCD}$ space, by building upon the transformation
rule of the Bakry-\'Emery condition under time change. We apply this result to
show that our previous results on the limits of closed Riemannian manifolds
satisfying a uniform Kato bound carry over to limits of complete manifolds. We
also obtain a weak version of the Bishop-Gromov monotonicity formula for
manifolds satisfying a strong Kato bound.
