Is USENET still USENET, even? That is, are there still nntp servers propagating the messages to "thousands of machines throughout the entire civilized world"? Or does everyone go to Google Groups to use it?

Yes, it's still possible to use Usenet independent of GG.

For example, in the early 2000s, I was doing a lot of reading of early Web/Internet sociology, nerd culture, etc, got very curious about what Usenet was really like (I understood all the basics and a lot of details like scoring files, but there's nothing like using something to get a feel for it) and discovered my local ISP had a NNTP server up for a decent chunk of Usenet (the main omission being the bin hierarchy). A few hours of meddling with Thunderbird and later, mutt...

It worked reasonably well and I understood why it was so dominant in its day, but spam was still a big problem compared to regular mailing lists and if my ISP didn't have a server up, I'm not sure how I would have gotten onto Usenet at all - there are few free servers these days.

No-one would invent it today, except in the form of a heavily decentralised and encrypted medium for secret discussion.

Still works pretty well for that. A fascinating example from 2005+: https://web.archive.org/web/20130119025623/http://dee.su/uploads/baal.html