When someone says "Sorry, not sorry" they are still sorry for something.

The first "sorry" is sorry as in "I'm sorry you found that offensive" which isn't a genuine expression of sorrow, nor is it an apology.

Its ambiguous, but it seems to expresses the speaker regrets not feeling regretful about the topic, as if to acknowledge that one might (and maybe should) sympathize with the other party, but in fact does not.

Depending on the context, it might also merely express that speaker is an asshole.

No they aren’t. It’s just an edgey way to say “fuck off”.

As a parent I say this about my kids all the time.

"And then he threw a tantrum because it was time to go, you know the exact thing I warned him about 5 minutes prior, and 15 minutes before that. Sorry, not sorry."

I like to internalize this as a victory, and the utter humiliation of the person who offended me. They said "Sorry." That's admitting defeat!

Do people still say that? I thought that got played out years ago lol

It's just a buzzwordy way of demanding that everyone notice their shitty opinion about something people probably didn't care about that much to begin with.

When they say that, they are an attention-seeking asshole.