Honestly, the relationship between what groups think of you and your poll numbers is usually pretty opaque.
Part of it may be the high default Apathy in the NAF scenario.

Ok, turns out there WAS something I was missing. You see, every voter is either in your party, the opposing party, or "none". Because they start so overwhelmingly against, you, they almost all join the other party, and if they are in the opposing party, they will nearly always vote for them or else stay home, even if they approve of you 100%.

Yes, if they approve if you enough, they will switch from the other party to "none" and then from "none" to your party, but that takes time. So it's important to get your approval up *FAST* enough for the people to decide to switch affiliation.

This means that my strategy of passing "just enough" to get rid of red buttons was a bad idea - it makes more sense to utterly smash the red buttons asap then repeal the excess policies later if it will increase approval.

This is actually a part of Democracy 3 and not just this mod, but because the base game is so easy it's basically unnoticeable by default.

I managed to double my approval despite group appeal barely changing at all:
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=766602718
..but I still lost the election, thanks to a blown media stunt.
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=766602651