The officical Apple support worked the problem through with me and ended up doing the update in recovery mode.
This means you have to restart your device into recovery mode (My iPhone: Switch on and hold the side button, press volume up then volume down after the logo appears while continueing to hold the side button. After a while the recovery mode is shown) and connect it to iTunes. Then choose "Update" from the given options and prepare for a long update process. Be aware that this might lead to a factory settings reset (iTunes will give you this warning too) if the process fails.
Doing it this way kept at least all settings (including registered ApplePay-cards) and caused no trouble as far as I noticed. I assume they expected that this procedure would be necessary only once, but on the current update (14.2) I ran into the update problem again.