I didn’t get that the IDE is running on both sides, if that’s true. Wow.

Yup! There's a language server and file server running in the sandbox that the editor on the frontend interacts with.

This is why most IDEs nowadays ask you something about "trusting files" when opening a project. They tend to lick and run on everything in there (at least for dynamic-ish languages, and maybe not "run" intentionally but do stuff which is arbitrary code execution more or less by definition) to analyze the code.