First, the doors don't open when I unlock them with the key. The mirrors also don't fold out. After I insert the key in the ignition and turn it, the car doesn't start. I get a message on the navigation screen that there are battery problems and that I should check the fog lights. If I remove the key, insert it again and try once more, the car does start. After that the car runs fine and I don't get any error messages, but the service light stays on. It then goes away by itself after a while. If I first disconnect the positive terminal and reconnect it before starting, everything is also fine and the car starts right away without any errors. Very weird!
I thought the battery was the problem. I measured the voltage and it was about 11.5 V after a night of standing (not measured directly at the battery terminals). Once the car is started the voltage almost immediately rises. If I turn the car off and measure again, the voltage is well over 12.5 V. Because of this behavior I thought the battery was slowly discharging.
After I installed a new battery today the problem remained the same. Because the old battery was disconnected anyway, I measured directly at the terminals and, lo and behold, it was above 12.5 V, so no problem with the battery.
I've also connected an OBD reader at different times, but it doesn't show any fault codes. I'm not sure where to look next. Does anyone have a tip or an idea?

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