This item is still in the works.
Also, thank you for the additional feedback. I will circle back to the feature team and provide a new update soon.
Currently we can only add lists that are inside a team, which doesn't really work for us. We have lists we work on that are present on other sites (e.g. time tracking).
Adding them as a website works but it's really clunky, it would be great if it was added as a SharePoint list.