Board Thread:Theories and Speculation/@comment-6769189-20200705100921/@comment-31715856-20200709012814

OP is wrong. Hamura and Hagoromo inherited Kaguya's chakra, so they almost certainly had Six Paths chakra. They already had a seeming inherent mastery of all the transformation types, which is pretty much default to Six Paths users. This is somewhat hinted in the anime, with Hagoromo already having been able to sense natural energy and mastering Sage Mode incredibly fast.

Secondly, Madara and Obito were trying to get the full power of the God Tree. Madara confirms this by noting that Obito began the process quickly, without having all the Biju Chakra, and we later see why: it lengthens the time it takes for the God Tree ti bloom its Rinne-Sharingan eye by 15 minutes. Naruto being given SPSM (this is confirmed in the databook, and obvious in the series, don't know why it was questioned above) doesn't have some other explanation related to the Demonic Statue. Naruto was given SPSM because that's all Hagoromo could give him. He was just a roaming soul. He didn't have, like, an extra Gedo Mazo, nor any Biju Chakra. He just granted Naruto the power of the Six Paths chakra so he could fight Madara/Kaguya, allowing Naruto to use Six Paths Senjutsu via that transformation.

Sasuke isn't a Six Paths senjutsu user because he has no ability with Sage Mode. But he does have Six Paths chakra, he says it directly in the fight with Kaguya, and Black Zetsu says Naruto and Sasuke have "Six Paths powers". What relation this has to Senjutsu Chakra (if any) is unclear. The databook just suggests "Six Paths" is some kind of reference to Yin-Yang Style. You can even see this in the seal that defeated Kaguya - Six Paths: Chibaku Tensei, a YYR technique. And that the Uchiha and Senju clans, the most "direct" descendants of the Sage of Six Paths, inherit a predilection for one of the components of the YYR style.