the commentator im reading also agrees with badarayana, and basically says that what sankara calls sheaths are not really that (although sankara doesnt consider them literal sheaths either but a chain of dependencies/limiting adjuncts) or even embodied selves but are metaphorical "selves" with the exception of the anandamaya, a pedagogical device for "men of small intellect" to understand degrees of subtlety with interiorization. my opinion is that either could work! imo there are no true ontologies except Brahman, only functional considerations, and both approaches work functionally. so many sources misunderstand this and believe in literal sheaths.