I am creating a GNOME Shell Extension and want to use languages like C++/Golang rather than JavaScript to create it. It is also acceptable if I can somehow call/use the C++/go executable in my extension.js. Please tell me if this is even possible and if yes how?
The short answer is no.
You can't ship binaries with a GNOME Shell extension, because they are architecture dependent and can't be properly reviewed. You could write a library with GObject-Introspection and ship that separately, but still not bundled in an extension for the same reason.
If you're tempted to ship a binary with a GNOME Shell extension, there's a good chance you should just be writing an application.