Technically, I think the Internet is considered a mesh.

I know of nothing trying to replace the Internet, but some wireless projects like Amateur Radio Emergency Data Network (technically can't use encryption on amateur radio bands), Meshtastic (messaging), MeshCore (messaging), and Reticulum (messaging, simple pages, BBS-like stuff). Any community could also try to set up a wifi mesh with something like the BATMAN protocol. Wireless meshes have all sorts of problems though. They must be carefully planned to get decent bandwidth because everyone's using the same "wire" (radio bands). Also, governments could easily jam or DoS them.