Mahāsāṃghika

In this capacity, he would have lived at a monastery with at least some, perhaps mostly, Mahayana practitioners while being called to advise the king on various decisions.

It's likely that the monastery was nominally affiliated with sub-schools of the Mahasamgika sect of early Buddhism, which was an interesting group.

If you remember from episode 121, what were the Nikaya schools, linked in the show notes, the result of the first schism of the Buddhist community was the emergence of two Buddhist groups, the Staviras and the Mahasamgikas.

Briefly, the schism was over whether certain precepts needed to continue to be followed.

The Staviras said yes, but the Mahasamgikas said no.

This set the Mahasamgikas as the quote-unquote progressive side of the schism, which continued as Mahayana eventually emerged among Mahasamgika practitioners.

The fact that Nagarjuna was likely Southern Indian, likely served as an advisor to a king of the Satavahana dynasty in the second or third century, and likely encountered early Mahayana is all that is known.

And even this is all educated speculation.