The majority of those in Colchis and Black Sea region were Greek by identity after colonization right up until the exchange. We can't tell for sure what genetic input is like there but it's safe to assume that it's fairly minimal. I've run across a few Pontic Greek GEDmatch results myself and they basically come up as Laz as you would expect.
Not really sure if you are agreeing with me or not. They were Romans (Byzantine-Greeks) by identity though if that is what you mean.