Since completely re-installing of Fairphone Open OS (including upgrading to 19.08.1), the bug is gone. So it was a software issue, but fixed either by the upgrade, or by the full re-installation.
For the re-installation, I did not only do a factory-reset, but a full wipe of the system partition; I followed the instructions here: 🇬🇧 🇩🇪 ✏ Installing the Fairphone 2 from scratch in case of failure / Komplette Neuinstallation des Fairphone 2 im Fehlerfall.
My main goal was to get rid again of the OpenGApps I had needed before but not anymore; as a nice side-effect, now this bug is gone, and also another where the Music app would always crash. What wonders re-installations can do 