I’m not sure I understood the question, but the infra-Bayesian update is not equivalent to updating every distribution in the convex set of distributions. In fact, updating a crisp infra-distribution (i.e. one that can be described as a convex set of distributions) in general produces an infra-distribution that is not crisp (i.e. you need sa-measures to describe it or use the Legendre dual view).
I’m not sure I understood the question, but the infra-Bayesian update is not equivalent to updating every distribution in the convex set of distributions. In fact, updating a crisp infra-distribution (i.e. one that can be described as a convex set of distributions) in general produces an infra-distribution that is not crisp (i.e. you need sa-measures to describe it or use the Legendre dual view).