Just as a suggestion for implementation: I would advocate for this to be a standalone extension.
The "GitHub Autolink" extension does not actually interact with GitHub API at all, it's completely "client-side" (or maybe rather "flarum-side"). Therefore I don't think it makes sense to add interactive features unless there are plans to do much more with the extension by retrieving rich previews for every links or something like that.
Incidentally, my Rich Embeds extension already has a GitHub integration that retrieves dynamic data from GitHub API for posted links. It shouldn't be very difficult to add the README content to the preview that's already being generated for links.
The potential issue I see is with licensing. You might not be allowed to embed a README file content. So you need a way to moderate and redact specific READMEs, and/or maintain a whitelist of allowed repos. Even if allowed to copy the README, the extension might need to also parse the repo license (luckily, I think GitHub already provides this information in their API) so you can display the license alongside the content.
Then of course there's the matter of refreshing the content. Do you fetch it only on request and cache it for a given time, or store a permanent copy that's updated from a scheduled task? The shorter the refresh rate and the greater the number of README links, it could quickly require a lot of server resources.