That bug is real and biological. Doctors have supposedly operated on them and they contain Dio's cells, so I think it's more of a vampire ability just like how his head had tentacles and stuff before. I do agree that his power is stronger and perhaps a combination of all the Joestars though. For one, he can take spirit photos without breaking his camera (I'd argue that to mean better control over his ability).

As for the genetic thing, another way to think about it is that all the "vine" Stands are all primarily connected to Dio/Jonathan's link while Jotaro's could be one that manifested from his own powers. Indirectly you could say that he inherited his powers from his father (or at the very least the genetic material), so that's correct too.

Also, [general message] please do not spoil even in reps.