there's an uninterrupted presence of greeks in southern italy from those initial greek colonies to the present day. the character of this presence has changed quite a bit though, and exactly where too. of course ancient colonies were city-states, and its thought the pretty immediate surroundings were habitated by italians, and this didn't change when the Romans conquered italy. Romans liked greek though so besides a lot of them getting enslaved greek cities survived until hellenistic civic culture goes into decline in late antiquity.

in late antiquity greek italy is briefly part of the gothic kingdom but afterward is the portion of italy most securely held by the 'byzantine' (greek-speaking now) romans and undergoes the same process of deurbanization as the rest of the empire; which is when greek language really gets emplaced in the countryside. ironically after the normans who conquered sicily kick out the roman government, its the cities who most directly interface with state authorities and trade & abandon greek while the peasants speaking greek don't. modern griko are the most podunk rural villagers in southern italy

so idk are they the descendents of Sybaris & Herakleia or medieval roman ruralization? they certainly ain't city folk like ancient times, the OG's were pagan & these modern ones are latin caths, & theres no geneaologies going back that far so :shrug-outta-hecks: its subjective