The thing that's really keeping me in Cursor (vs decamping for Zed) is NOT the Cmd K or the sidebar chat. It's actual Cursor's Tab autocomplete model. I've tried many other tab completion models and Cursor Tab blows them out of the water. Supermaven's new release is promising, however.
For the use-case you're solving for (issues with code-privacy), I think something like https://codeium.com/ does already allow for on-prem deployments with enterprise support. I'm trying to think of who would be served well by a fork of VSCode vs Continue.dev or something like a codeium VPS deployment.