I definitely call the mind (but also consciousness) natural. I would say that also materialists would agree with me. There is however one tiny detail that allows me to embrace naturalism and modern science without "hard problem of consciousness" as well as without resorting to appeals to anything even remotely supernatural. In short, it's the fact that phenomenal world does not feel solid because matter is material but because what we call matter is just a set of overarching rules of manifestation.

https://senderspike.medium.com/fractal-evolution-b0d66bacff40

As for Vedic view -- I like it too. It's the only tradition that is explicit in terms of knowledge, way to reach it, etc. Unlike Buddhism, which only leads one to realization while remaining silent on its nature, Taoism, which is basically Karma yoga plus a tiny bit of cosmology, or Abrahamic tradition, which is an inscrutable maze and IMO completely unsuitable as a manual for a lay person, Vedic tradition lays out the whole affair in no uncertain terms.

This explicit approach has, however, one serious drawback -- by spelling out the absolute as Brahman it incites seekers to search for it as an object (I guess that's the reason why there is Buddhism with its doctrine of anatman as no-self and why Buddhism is almost completely silent on the nature of absolute). And of course there are some parts of Vedic tradition that have been superseded by modern science (which, however and again, can be ascribed to the fact that those parts were simply misinterpreted by later commentators).

Just to name a few -- transmigration of soul or the subtle materials of mind you've mentioned. I won't go into details here (pls. see the links below if you are interested), but mind and brain are literally one and the same, or rather mind is the function of brain. As with computer software, which is at all times just the state of underlying hardware, mind is at all times the state of brain. Thus the unity of existence is palpable (and observable!) even in "relative realm" of manifested phenomena.

https://senderspike.medium.com/heaven-on-earth-7d83596d4a0b

https://senderspike.medium.com/mind-brain-and-consciousness-9127f14dea4

https://senderspike.medium.com/absolute-equivalence-b4584dc2e290