The hey day of African chattel slavery followed medieval period, a project of horrific proportions carried out by the society that followed medieval Europe.
As I recall Slavery was legal in medieval Europe but not as widely practiced as serfdom at the time but both were forms of coerced labor (serfs were "slaves of the land" - couldn't leave and had to provide labor or goods). I mean sure, the particular institution of chattel slavery was dying out but this more a matter of "we need something simpler" than any impulse to improvement or any actual improvement.
[1] https://en.wikipedia.org/wiki/Middle_Ages [2] https://en.wikipedia.org/wiki/Abolitionism
https://en.m.wikipedia.org/wiki/Slavery_in_ancient_Rome https://en.m.wikipedia.org/wiki/Slavery_in_medieval_Europe
A big hindrance to seeing continuity is that popular knowledge of "romanness" is so focused on the late republican/early imperial era and there is surely not much visibly continuity between early medieval and a snapshot of the Roman state outdated by several hundred years.
[1] https://en.m.wikipedia.org/wiki/Slavery_in_the_21st_century