I use Claude Code Web almost exclusively for personal projects -- I’m guessing that’s pretty much the same interface but in the cloud -- and hardly ever run anything locally. Nicer UI than a terminal, real sandboxing, and it doesn’t tie up my computer. It’s just a remote agent that can make GitHub PRs.
But even worse for private stuff than using cloud inference to begin with, since it presumably has to clone the repo, have write & Actions access back, etc.