For example, I’m Jewish. If a non-Jew makes a “Jews run the world” joke, it’ll likely come across as highly anti-semitic. If I were to make that joke, I’d stand a decent chance of getting a laugh

You mean to say that the Jews that run the world have access to exclusive jokes?

Punching down works when it's setting up cultural context for a much bigger punch in the other direction. Bill Burr walks that line pretty well most of the time imo. He'll take small jabs at some low hanging fruit and then the punchline is that he's actually a terrible person and you should feel bad for laughing at him. Sometimes at least. Other times that whole schtick doesn't quite land.

Punching down is never funny

clearly you have never slapped a dwarf

on a serious note, you are wrong and your categorization is arbitrary, you are playing joke police.

for example, Ricky Gervais had an entire bit about Caitlyn Jenner, is that punching up or punching down? because Ricky is more famous and maybe even more wealthy than Jenner and also a white male and also didn't kill anyone with his car as far as I know, so that's punching down right? or we is it punching up because we dislike Caitlyn Jenner for her pro-republican stance?

When is your Netflix stand-up special going to be released?

Did Chat-GPT write this?

The other punch style is the self punch. This is where you make fun of yourself or your own “group.” For example, I’m Jewish. If a non-Jew makes a “Jews run the world” joke, it’ll likely come across as highly anti-semitic. If I were to make that joke, I’d stand a decent chance of getting a laugh. (Well, assuming that I had basic comedy skills.)

This is also potentially pretty bad, though. It is a hard line to tread, to make fun of the absurdity of the claim, without, at the same time, validating the premise, for those who believe it, part of why being a comedian is so hard. You have to attract the people who would otherwise believe such a thing, and then illustrate the idiotic absurdity of the claim itself, and you know, the idiocy of the believers of it. You have to make them face it. If you just end up pulling off an exclusive "self-punch", and especially one against "your group", it's very likely to just be accepted/seen as you selling yourself and your group out, in order to validate everyone's preconceived notions, even if that wasn't necessarily your intention. Just like that dude who made a country song a while ago about politicians in washington being shitty, but also being about people on welfare eating cookies or whatever. A conservative narrative got pushed about his song, despite how he wanted, retroactively, for that not to be the case.

https://youtu.be/F8yV8xUorQ8

Basically this.