Well I am on the millennial/Gen Z cusp, and I think the new "old web" is a recreation of the corner of the Internet that puts humans before bots (as opposed to faithfully recreating it). Then again this website feels like it's doing a little too much.
Or too little... aside from themes and music and a chatbox there's not much to it.
What you're describing is the IndieWeb, I feel like if you're going to call something the "old web" the effort probably should be to actually recreate it a little more faithfully