I understand that it’s the MagSafe or whatever it’s called, method of charging that is causing the problem. The theory is that the BMW cradle does not supply enough power. When I put my iPhone 13 Pro onto the cradle, the green charging light goes on and then switches off. It then spends the rest of the day switching on and off, during time which my phone slowly flattens itself. This does not happen with my iPhone 11, which charges just fine.
The work around is to put the iPhone 13 in the cradle but power it via its USB connection. Of course this requires a separate lead and power source.