David_S

Thanks for the reply. Looking into it more just now, I see what was causing my confusion. I just re-tried editing some buttons that I had added while developing... removed the link, and re-added to the page using SS's chooser... and it inserted the relative link, but kept the demo URL when hovering over those buttons (in the editor).
However, when loading the actual site with its public URL via a private window, those links DO show the correct URL.
I was getting worried when I saw the links on SS's backend weren't updating, when that's not what I should've been looking at!
Thanks again for helping me figure that out 🙂 

If you put a link in to a button or text using just the URL slug (or via the assisted process) then it will work correctly. By correctly I mean that it will not change the domain name that you are viewing the website with. In the backend or when accessing the website via the built in domain it will remain on that domain, if you visit the website on your primary domain then it will remain on that domain.
I would recommend against putting the full domain name in to links as it will force the website to reload completely each time, and it'll cause you problems when editing.

Yep, just have to hope a future version of Safari treats this use case better, I guess 🤷‍♂️ -- thanks Paul.