The oops pr for "No outer loop update for B" was merged: https://github.com/JCSDA-internal/oops/pull/3010 .
I think this can be applied to all of the existing variational applications for current workflow design.
However, we still need to be careful about the other case (i.e., the resolution of inner loops change over different outer loop or B depends on the first guess). Or if we can add some check ?? warning comment ??