In our system, non-staff users have an empty /tags page, and they also see no tags in the edit tags navigation pop-up. Users can use tags to tag posts, see the tags in tagged post, click on the tags etc. etc.
We don’t use tag groups, there are no default navigation tags. We may have played around with those settings in the past, so I suspect it is some setting I don’t find, or an artifact/bug from past experimentation. Any hints where to look?