There’s very much still new punk, but it’s old enough that what you described probably should be thought of as classic punk. It’s evolved, grown, changed, and split. You’ve got plenty of bands still screaming similar to the old school stuff, but you’ve also got stuff like against me, rage against the machine (yeah it’s rap punk), and my mind is blanking on other modern well known punk bands, but then you’ve got punk descended genres that are still punk like folk punk and riot grrl as well as genres like goth and emo

I think it’s better compared to metal. It’s an offshoot of rock that branched, evolved, and stuck around with a certain type of people