@takayuki Miyoshi: thank you for the suggestion!
What I did:
Installed, activated and successfully configured the WP Mail SMTP > The problem remained.
Updated all plugins. > The problem remained.
Deactivated all plugins. > The problem did not occur anymore.
Activated all plugins one by one. > The problem did not occur at all anymore.
Somehow it is solved, with all plugins activated. So at this point my motto is: if it ain’t broke, don’t fix it.
I hope this helps others facing the same problem.
