This is indeed one important line of inquiry, for which conclusions may be fetched from that other thread.
But there may also be other lines of inquiry, taking the issue from a different angle. For example, if the Buddha did come up with his own new style of meditation, that would explain SN 41.8, which otherwise remains puzzling, as that would imply that Mahavira didn’t know anything about a type of meditation supposedly practiced by various types of ascetics of his time, despite being obviously prone to engaging in debates with them:
Nigaṇṭha Nātaputta said to him, “Householder, do you have faith in the ascetic Gotama’s claim that there is a state of immersion without active nor passive thought; that there is the cessation of active and passive thought?”
“Sir, in this case I don’t rely on faith in the Buddha’s claim that there is a state of immersion without active nor passive thought; that there is the cessation of active and passive thought.”
When he said this, Nigaṇṭha Nātaputta looked up at his assembly and said, “See, good sirs, how straightforward this householder Citta is! He’s not devious or deceitful at all. To imagine that you can stop active and passive thought would be like imagining that you can catch the wind in a net, or dam the Ganges river with your own hand.”
I took the liberty here to edit BS’s translation, as his doesn’t make much sense to me in this passage. Otherwise we have to assume that Mahavira was both so ignorant of meditation techniques that he didn’t know the second jhana existed, but at the same time knew the very specific vocabulary of meditation, which would have been so esoteric that even the EBTs do not have a single instance of these words used in that purported meaning.