Disclaimer: Haven't used the tools a lot yet, just a bit. So if I say something that already exists, forgive me.
TLDR: Targeted edits and prompts / Heads Up Display
It should probably be more like an overlay (and hooked into context menus with suggestions, inline context bubbles when you want more context for a code block) and make use of an IDE problems view. The problems view would have to be enhanced to allow it to add problems that spanned multiple files, however.
Probably like the Rust compiler output style, but on steroids.
There would likely be some chatting required, but it should all be at a particular site in the code and then go into some history bank where you can view every topic you've discussed.
For authoring, I think an interactive drawing might be better, allowing you to click on specific areas and then use shorter phrasing to make an adjustment instead of having an argument in some chat to the left of your screen about specificity of your request.
Multi-point / click with minimal prompt. It should understand based on what I clicked what the context is without me having to explain it.