How aware of the existence of Buddhism and other Dharmic religions were the Jews in general around the 1st century BCE and 1st century CE?

In the wake of Alexander’s expansionism central Asia saw the development of Greco-Buddhism from the 4th century BCE onwards. Ashoka sent emissaries to the West, as far as the Mediterranean, to spread Buddhism. Now, there are Ancient western sources that discuss the presence of Sramana ascetics in Rome and Athens at the reign of Augustus, as well as early Church Fathers like Clement of Alexandria knew (at least vaguely) of the Buddha. So some people around the Mediterranean were aware, at least in vague terms, of Buddhism or Sramana traditions from India. But do we know how common was this knowledge in general? And were Hellenistic Jews and Jews in general aware of them? And if Buddhism wasn’t commonly known, were there some Jews who knew (at least vaguely) about it?

P.S. This question is an adaptation from another more broad question I asked on other subs, that included Greeks, Romans, early Christians and Gnostics, which didn’t get properly answered or didn’t get answered at all.