Use Git from inside Mindex, on a repository that is ordinary in every way.
Mindex can initialise Git in the vault when you ask it to. It will not do this on its own.
Stage what you want and commit from the Git panel. Everything is a file, so a commit is exactly what it looks like: the notes you changed, the types you edited, the context files the background job rewrote.
Add the remote and push. This is the same operation you would run in a terminal, and you can run it in a terminal instead — Mindex does not own the repository.
Authentication uses the credentials your machine already has. If pushing fails, see Git authentication.
.mindex/cache.json and .mindex/tmp/ are derived and can be ignored:
.mindex/cache.json
.mindex/tmp/
Keep .mindex/types/ and the per-folder context files. They are part of the
vault, and someone who clones the repository should get them.
Push from one, pull on the other. There is no Mindex cloud, so this is the recommended route — and because the vault is ordinary files, any sync tool you already trust works too.