Because vscode and cursor use the same settings file, but cursor uses open-vsx, it becomes impossible to write a .vscode/settings.json or .vscode/extensions.json that works for both vscode and cursor.
The Cursor docs specifically suggest using the same extension ID in both the visual studio marketplace and open-vxs:

I think it would be best if this extension was also published to open-vsx under the "jakebecker.elixir-ls" id.