Claude Code Web uses the Github connector to check out repositories, make commits to them, and open a PR. Unfortunately that's about all it can do with it currently, I was working with it the other day and found it somewhat disappointing that it can't read and reply to PR comments as that would be a really natural way to handle refining the code that's been written.

I tried getting it to use the `gh` CLI to do so but it either doesn't have the right permissions on its token or the requests are being intercepted and filtered by the sandbox it's in. I eventually dumped all the comments as JSON from my desktop and pasted it in at which point it handled them fine so it's certainly capable of working that way.