I saw him test out some material for this at the Cherry Lane back in 2019, and ever sine the pandemic he's been continuing to test out material for it via his podcast, and I believe he also performed some version of it at City Winery last fall, though I didn't get to see it. Still, it feels like it's been developing right before my eyes, which is so fun. I'm excited to see it in its final form!
As for the thread question, I think there's a 99.99% chance that he'll bring the show in NYC. He lives in NYC, he performs here all the time, he has a long history of doing Off-Broadway shows, etc. I think it's very safe to assume the show will play NYC in its final form.
As for whether it will come to Broadway...a very different question. The New One did very poorly at the box office, but then again, I'm sure it was also extremely cheap to run. Plus, I'm not sure how the financial model worked exactly, whether or not Netflix helped finance the show so they could film it, and how that might have affected their bottom line. I don't personally know. But bringing any show to Broadway is a financial risk, and it's possible that they'll feel better just doing a month or two at Cherry Lane or somewhere like that.