"Baby" vs "宝贝" - coincidence?
Interesting, but this is a coincidence.



Baby comes from a reduplicated Proto-Germanic root *bō-, which is cognate to English boy, appended with a diminutive suffix -y.

寶貝 comes from the meaning rare/precious seashells; this usage is attested at least since the Han dynasty. As a term of endearment, this started appearing as early as in the novel Dream of the Red Chamber, written in the 18th century.