VS Code does actually already have this. I use it in Antigravity IDE.
https://marketplace.visualstudio.com/items?itemName=anthropi...
https://marketplace.visualstudio.com/items?itemName=anthropi...
The biggest features are the ability to view diffs in the IDE instead of the CLI and sharing Roslyn analyzer compiler errors and warnings to the CLI with file and line/char span information to help with debugging.