There's been a few good answers on similar topics that might tide you over while we wait for an answer:

n ancient Rome what was the difference between a freedman and a citizen? by /u/bryminski

suppose you're a rich roman (AD250) and you decide you're really really fond of one of your slave children and you want to have them educated and made into a normal free roman, like as if they were your own child (legitimate child). how unusual would this be? to what extent is it legally possible? and Slavery in Ancient Rome, how did slaves earn money to buy their freedom and how common was a slave to be a freedman in this way? by /u/XenophontheAthenian

Additionally status and citizenship rights were passed on hereditarily. And children usually inherited the status of their mother but at the same time individuals could be manumitted and become freedmen. Citizenship was also granted to non-Romans with service in the auxiliaries being a notable route to citizen rights. Another route was adoption where the individual inherited the status and family of their adoptive father.

I wouldn't ever compare Roman slavery to US slavery because freedmen didn't have to deal with any racial stigma, and even though slaves were taken in conquest or purchased from foreign lands the preponderance of slaves in Roman Italy were probably Italian. There's also a lot of evidence for Hellenic slaves but a. this has as much to do with a bias in our surviving information and interpretation of it and b. Greeks were not viewed with anything approaching the racism that African Americans in the US were in the Antebellum South.

You really didn't have an ethnic caste of slaves or second class citizens once freed so no it wasn't much like that at all, and I'm not sure what you mean by "blending into the broader population" given the context. The overall affluence of a freedman would depend on who their master had been, what their occupation and station in life was, and who their patron was. Freedmen often married other freedmen but this is more reflective of the tendency for people to marry within their social spheres and strata in ancient Rome and possibly of the fact that these individuals may have had relationships going back before they were freed.

Funnily enough, the problem woth our understanding of manumission of slaves in the Roman Empire/Republic is that affluent, socially mobile, literate slaves from Greece and the Greek East are seen as the archetypal freedman. It is true that some freedmen like Tiro who had been the secretary of Marcus Tullius Cicero inherited assets and did well fir themselves in life. But we can't and shouldn't expect this for all slaves since not all slaves had the same opportunities or skills before, during and after their enslavement. We know that freedmen engaged in Roman society culture based on art, funerary inscriptions and dedications by/about freedmen, and there are numerous literary references to freedmen in various situations. However this brings to light the issue with all of our syrviving evidence which is that it disproportionately represents the more literate and affluent strata of society. Stereotypes about freedmen being uncultured and amoral abound in Roman literature so it wasn't all peaches and cream for how freedmen were seen by the rest of Roman society, and many may have had to contend with xenophobia or negatives attitudes about their original status as a slave and any foreign origins (if they had any).

I still think it's fair to say that the difference in the social status of a freedman in Rome or the Southern US was markedly different. Slavery was a supremely degrading and devaluing practice though, something that in theory no citizen would ever be subjected to.