The last axis contains the related variables of a MvNornal, so a 1x100 mvnornal reflects a single vector draw. A 2x100 MvNornal would reflect two independent draws, each of which is a 100-long vector whose elements are related to each other (not statistically in this case because of the diagonal covariance).
The logp of a single mvnornal is a scalar regardless of how “long” it is. For a 1x100 you get something with shape [1], for a 2x100 you get something with shape [2]