Roman tradition still forms the basis for many police institutions across much of Europe. Most of Europe and the Americas didn't abolish slavery until a few decades before the US did. Some actually didn't abolish it until decades after US emancipation. One could make a claim that their police forces are rooted in enforcement of slavery, in the same vein as the South. And even stronger ones for much of the Middle East and North Africa, some of which didn't actually make slaver a crime until the 2000s (I kid you not [1]). If you believe what is going on in Western China, you could argue that slavery is still practiced, under the watchful eye of law enforcement. My point is that pointing to the history of policing in the US as uniquely tied to slavery is pretty disingenuous if you're taking a good faith reading of the history of policing. It's acting like there isn't a country and a half between the police forces of 1860 and 2020.
https://en.wikipedia.org/wiki/History_of_slavery_in_the_Musl...
That's essentially summarizing the article: slave patrols existed in much of the south, but claiming continuity with today's police is a very big stretch, to the point where it's only poetically true.
Yes, policing in Southern slave states has some roots in slave patrols.