The only feasible way to support this is as an advanced option, since changing the default storage location would break backwards compatibility. A new StoragePath setting has been added - by default it still points to the old location (%AppData%).

If you're feeling adventurous, you can override it in appSettings.json (preferably in appSettings.override.json) and set it to . to store everything next to the portable executable.
Just make sure to manually move your existing data from %AppData% to the new folder.

This is considered an expert-only option, so use it at your own risk.