Tagging in Media library

The tagging in the Media library (is that the right English word for the German "Mediathek"?) doesn't work. I enter a tag-word, but it will not be saved.

I think this is a known bug (I seem to remember being one of the users who reported this some time ago) - you need to tag directly in Amber and this will subsequently sync down to Media in the Logos desktop app.    

What do you mean with "directly in Amber"?

the user Media - and I assumed you were writing about those, I don't see a way to tag the Logos Media - are stored in a cloud location called Amber and your stuff is available to you under https://amber.faithlife.com (which includes user Media uploaded through Logos, media uploaded in Faithlife groups, screenshots uploaded through the Amber icon in the forum software etc.) . There you can manage the tags, delete items etc. 

EDIT: found my old report and that FL has made a case for it (obviously not resolved yet): https://community.logos.com/forums/t/200992.aspx  

This thread is mentioned in the release note for Logos 9.14 Beta 1: the issue has been fixed and user media may be tagged in Logos now (and probably should be: the automatic tags associated by some AI will currently not be found in the Logos Media tool).