I think that may answer it. Pretty surely cookies are enabled.
However. I have 'Reset' Safari several times - i.e., emptied the cache. Useful to be sure new previews of a dynamic page from DW will display correctly. Pretty likely cookies got trashed in the process.
In any event, I think that is the best working assumption. Which means the 'problem' is on my end, local here, and nothing useful for you all.
And now I will going forward remember: when clearing the cache - expect to be logged out!