golia, Oirats and Buryatia are properly Tengriist, while Sarig Yogir is accurately buddhist.
Tengriist manchus are a bit of an issue, they were shamanist until turning to "chinese folk religion" a.k.a Confucian in the game (I assume) when they became rulers of China. In my opinion, they should start as Shamanists and switch to confucian when forming Qing.