Git plumbing: Handle errors better

[N-o-Z]

We rely on git command output message to translate it into meaningful errors. This might become tricky in some scenarios:
#8345 (review)

[talSofer]

This can be prioritized as a tech debt, removing from the product backlog

[yonipeleg33]

It might be worth looking into formatting the git command output in a machine-readable way.
For example, commands like git status has the --porcelain flag, other commands like git log have the --format flag, and there are other helpful flags out there.

I've chatted about it with Perplexity, it might contain interesting information.