Just another tidbit: Some followers of Daoism (prehistoric Chinese roots) think that the Old Sage himself, Lau Tzu, legendary author of the Dao De Jing, later moved to India where he became known as Buddha.
The Preface to this copy of “Tao Te Ching” written in December 20, 1890 by JAMES LEGGE (Oxford) addresses some of the Tao / Buddhism / Confucian influences.
Hope that you enjoy his point of view and references.
https://archive.org/details/laozi_tao-te-ching/mode/1up