So, the slang that I (as a younger millennial) understood was:

capping/capaholics: I know “no cap” gets used to mean “seriously/honest”, so from context those become “lying/liars”

sigma: because talking about being “alpha” is too outdated, sigma is basically the new “alpha”, i.e., awesome people

yapaholics: yap isn’t even new slang. I reckon my boomer parents would know that one.

Everything else was just context. “There will be no fanum tax under a government I lead”. Either fanum actually means carbon, or more likely she just chose some random word that fit the metre of Gillard’s now-infamous line. Also: kinda disappointing to see her bring that up in this way as a former Labor Senator. And one who left the party not because of disagreement with Labor ideals, but because Labor political leaders today aren’t living up to those ideas…or even up to their own official policy and membership.

Anyway, I’m not sure this is necessarily gen z slang anyway. Maybe younger gen-z–older gen α? Definitely feels like the sort of thing you’d hear from a tween/early teen today, rather than from late teens/early 20s, and the youngest gen-zs are 12 this year.