Why are FaceTime calls failing on my MacBook Pro?

I also have the solution: In this case I remembered updating Mattermost some days prior to this FaceTime error.

In Mattermost (installed app, not web app) I couldn't share my desktop with colleagues. This was resolved by an update from Mattermost (version 5.11.0). But this most likely resulted in the issue with FaceTime, since removing Mattermost altogether seemed to have resolved the issue. FaceTime functions as normal again.

I hope this helps others.