F* existed before Project Everest, but Everest did power a lot of its development.
We have built verified systems and components in the TLS ecosystem, including parts of TLS, QUIC and related protocols, and continue to do so: https://project-everest.github.io/
I have not tried the VSCode stuff, but I did try the Emacs thing. Looking at the repo you linked, it looks like the first commit was last year and I left Jet in 2018.
The Emacs mode was fine, I didn't think it was bad, but it was still a tough sell to my team; none of them wanted to install Emacs, they wanted a Visual Studio or JetBrains experience. I'm aware that's an uphill battle, and maybe it would be a different story if the VSCode extension existed in 2018.
About the name: https://fstar-lang.org/tutorial/book/intro.html#a-bit-of-f-h...