The coherence theorem for bicategories, as usually stated, reads

Any bicategory $B$ is biequivalent to a (strict) 2-category.

It is possible to give an explicit construction of the strictification as the full image of its Yoneda embedding $y:B\rightarrow [B,\text{Cat}]$, see for instance this reference.

This seems like a natural construction, so I would expect an equivalence of tricategories

$$ \text{Bicat} \leftrightarrows 2\text{-Cat}$$

where the rightgoing functor is the full image of the yoneda embedding, and the leftgoing functor is the inclusion. However, I cannot find such a statement in the literature. If it is true, a reference would be appreciated.