I think having strong interpersonal conflict means you need to break down cause and effect of each “exchange”. This is sensical to normal gamers in physical conflict – I attack, I cause harm, I cause enough harm, and I win. What’s the effect of saying “Winston, are you sure your heart can take this?” – it’s non-obvious for social conflict to the players.

But yeah, DramaSystem might do that. And if you want something closer to what you know, Malandros is a PbtA Dramasystem hybrid that does a good job of covering both games.