Many deeply religious people might dispute there is a natural/supernatural distinction at all.

This can be a valid perspective, but this is also an entirely different thing from reducing everything to nature alone.

I agree that a system that's purely descriptive would probably not be a religion. But something that deals with subjective beliefs, and informs the believer about what they should do with their lives and what is truly meaningful, would have at least some similarities with religion.

I think what you are referring to here is much closer to myth in the secular sense, rather than religion. Religion does deal with the things you mentioned, but its approach to those things is informed by a metaphysical position. If we take some types of Buddhism as an example, there are indeed rules for personal conduct, a value system and spiritual practices, but all of this is justified on a supernatural basis, specifically attaining enlightenment.