But is there there a way to not only include the tags from the annoation in the note-text, but automatically add the tag from the annotation to the note-element when creating a note from an annotation?

No, this isn't currently possible, but it's a fairly common request.

Could you say more about how you would use this?

Thank you for your Support @dstillman!

My use-case would be for instance: Commenting or summarising a concept that is covered by a number of different papers. While reading the papers, I would mark the lines where the concept is mentioned and and add a tag for that concept in the annotations, then convert the annotations to notes.

With the tags from the annotations automatically synced to the note-tags I could filter my library for notes with that tag and then review the concept across the differnet sources. And more importantly I could also revise the tag-system; maybe add a subcategory or exclude one annotation from that tag.

Does this make sense to you?

I have to admit: I fear that I would stretch zotero too much with this kind of use-case. I am thinking of setting up a personal knowledge management in obsidian. Still, it would be very useful to keep the tagging in the annotations synced with the tagging in the knowledge management system.