Cloning git repo within an electron app, compiling a statically linked build of git

Your best bet is to use libgit2 and the bindings for Node.js. libgit2 is a library that can be compiled and run without any other dependencies and will provide most client-side Git functions, albeit at a lower level than command-line Git. It is widely used in a variety of contexts, although it lacks some features (like SHA-256 repository support).

The problem you'd likely encounter with Git on Windows is that Git requires POSIX tools, including a POSIX shell, to perform various functions. Windows lacks this functionality, so you have to ship it yourself, and even when you use something like Busybox, it still requires a bunch of space.

I will note that even if you use libgit2, you're still going to need to link a TLS library for your app to be minimally functional. On Windows, one is provided, but on Linux, I strongly recommend against statically linking a TLS library into your binary because they come out with security updates all the time, and you will instantly become responsible for updating your app immediately upon a new version coming out or your app will be a security problem.

Because typically these libraries (of which OpenSSL is the most popular) are not portable across Linux distros, you're going to need to ship a binary for each platform. You'd need to do that anyway, because if you're shipping Node or another runtime, it will also have a dependency on a TLS library and probably glibc, which will require this anyway.