You can do this today with OpenAI Codex, which is built into ChatGPT (and distinct from their CLI tool, also called codex). It will allow you to prompt, review, provide feedback, etc via the app. When you're ready, there is a GitHub PR button that links into a filled out pull request. It has notifications and everything.

There are a handful of products that all have a similar proposition (with better agents than OpenAI frankly), but Codex I've found is unique in being available via a consumer app.