How do you keep the experience consistent across VS Code, Cursor, and clones?
All the editors share the same VS Code internals and APIs, so once your extension works in VS Code, it'll likely work in other editors. The are different ways to distribute extensions for VS Code and clones, but that's a technical detail.
Design-wise, even if it's just VS Code, there are mutiple themes, dark modes, etc that may affect your content, so you have to keep reusing VS Code CSS styles and keep your own styling minimal so that the content look good on any crazy theme user might have installed. And on the web, you can carry VS Code theme variables to style things similarly to VS Code's base theme.