gh: Move away from using curl for patches and to GitHub API

:warning: This initially failing PR is an TODO item for `am/apply` commands. We need to switch them over to the GitHub API so that they won't have any external dependencies.

/cc @jingweno
We could test a `RoundTripper` by sending a request, like [what we did in `go-octokit`](https://github.com/octokit/go-octokit/blob/master/octokit/client_test.go#L10-L29). We then assert the headers, URL etc.