Tengrism and Buddhism aren't similar from each other sorry. Buddhism is an atheist religion without a god while Tengrists believed in one supreme sky god called Tengri. Tengrism is mostly characterized by features of Shamanism, Animism, Totemism, both Polytheism and Monotheism. Buddhism is more like an intelligent philosophy than a mythical religion like Tengrism
You shouldn't also forget that Tengrist Mongols attacked and killed many Buddhist Chinese people when they invaded and conquered China
Breakaway states of the Mongol empire like the Ilkhanids also adopted Islam when they were culturally influenced by Muslims. The Hazaras today are the desendants of these Ilkhanids and they're also Muslim, though they have sadly forgotten their language and speak a dialect of the Persian language today
The Ilkhanate, also spelled Il-khanate (Persian: ایلخانان‎, Ilkhanan; Mongolian: Хүлэгийн улс, Hulagu-yn Ulus), was a breakaway state of the Mongol Empire, which was ruled by the Mongol House of Hulagu. It was established in the 13th century and was based primarily in Persia as well as neighboring territories, such as present-day Azerbaijan, and the central and eastern parts of present-day Turkey. The Ilkhanate was based, originally, on Genghis Khan's campaigns in the Khwarazmian Empire in 1219–1224, and was founded by Genghis's grandson, Hulagu Khan. In its fullest extent, the state expanded into territories which today comprise most of Iran, Iraq, Turkmenistan, Armenia, Azerbaijan, Georgia, Turkey, western Afghanistan and southwestern Pakistan. The Ilkhanate initially embraced many religions, but was particularly sympathetic to Buddhism and Christianity. Later Ilkhanate rulers, beginning with Ghazan in 1295, embraced Islam.
Ilkhanate - Wikipedia, the free encyclopedia