While quickly checking how everything worked after the repair, I noticed the updated firmware version 11/2025.24 (iDrive 9). In this version, developers have added the option to disable the Auto Start/Stop function using a dedicated physical button 'Drive Settings menu' on the center console.
Now you simply need to hold the physical button button down for a few seconds. There are no longer any additional steps or taps on the screen required. The message that appears there is purely for information about the current mode and does not require you to press anything.