Tibetan and Han shared same genetic roots, so does their language (collectively classified as Sino-Tibetan languages). Legendly, in the dawn of human memories, the ancestors of Tibetan lost a tribal war against the ancestors of Han in the east and migrated west to a less-inhabited / less-suitable area as a result.
FYI: https://onlinelibrary.wiley.com/doi/10.1002/ajpa.23291 Note the PCA plot: https://onlinelibrary.wiley.com/cms/asset/6f245ebd-af27-4633...
The PCA plot only note two genetic variations. You could easily find similar plot just between northern and southern Han.
"Chinese was suggested to split away from Tibeto-Burman around 6 thousand years ago (kya) based on lexical evidence."
This is consistent with the cliche of Chinese having 5000 years of history if we consider the formation of the Chinese language as a foundation for the nation.