@gerhard No problem.
I opened a Guest window in Chrome (so, technically, a different user profile I suppose) and the problem persists when I log in with my usual Discourse user. In the same browser window, I created a new user in Discourse, then logged in: the favicon showed up. Then I logged off again (the favicon was still there), and I logged in with my usual user, and again the favicon disappeared. Very strange.
Regarding the certificate chain being incomplete: I’m not exactly sure what I need to do, I guess I forgot to upload a certificate file on the server, thus it gets downloaded every time?