Greek continuity from the BA cannot be evaluated properly with the crumbs of data that has been made available so far. Data from IA to the Late Middle Ages is completely lacking. We only have a limited amount of BA samples, and modern samples from Greece (very few used in studies for some reason).
The Antonio et al paper on Rome showed how modern results overlapping with IA or BA ones are not necessarily indicative of the former being descendant of the latter, as modern samples there overlap with IA and Republic-era results, but the intermediate periods show significant south-eastern and then north-western shifts. The authors attributed this to migrants from the East Mediterranean first, and from Central Europe later (which was not well-taken here I remember). So the overlap between IA and modern samples was at least partially coincidental. If we had from Rome, only the amount of data we have from Greece, many would now be speaking about genetic continuity from the Iron Age to today.
So far, it can only be said that modern Greeks are among the European peoples who plot near samples from BA Greece. This hints, at the very least, to shared ancestry between modern Greeks and those samples, but this could be due to either modern Greeks descending of those BA populations, or of other populations that had similar ancestry components, or (more likely) both. But it does not prove either possibility. Just like in Rome, it may be that the modern and BA similarity has a more complex explanation.
There are already small hints that favor a similar scenario in mainland Greece, while the islands may have been largely unaffected. We now know that Steppe-related ancestry arrived to the Aegean during MBA, as it is missing from earlier periods. Therefore, new samples from MBA mainland Greece likely represent some of the most Steppe-like prehistoric populations of the region, and such ancestry was almost certainly subsequently diluted through admixture with non-Steppe peoples of the Aegean. In fact, Mycenean samples of the Late Bronze Age already show diminished Steppe-related ancestry, and this trend probably continued through the IA and into Antiquity. So if the latest study showed that modern mainland Greeks can be modeled as the heavily Steppe MBA samples with some additional Steppe ancestry, it is probable that a larger Steppe-related component is required to model them with IA or Classical period Ancient Greeks, which would suggest important influxes from the north in subsequent periods.
