Negative diplo means you are a war monger because you take a decrease for each captured setlement but doesn't immediately lead to low relationships with every civ. You can always declare a formal war as a mil focused playthrough to avoid that initial decrease in war support. I would say that paying diplo for war support is like internal propaganda to raise the happiness of your pop. I never noticed a decrease in relationships with other civs based on low war support. And usually resistance groups only form when a war is going very badly. Partisans gaining strength on negative war support would be like the resistance gaining strength while the rest of the country falls apart.

I think we understand war support differently then. For me, fighting against oppressors is reflected in having high war support, because being the target of an invasion gives you war support and so does having good diplomatic standing.

Negative war support means you're a warmonger and everyone hates you.

I associate partisans with a resistance movement. Please correct me if those are two separate things. But it would be interesting if the partisan unit gained strength on negative war support to show their increased determination against invaders/oppressors.