Based on the suggestions I received here and by email, I was able to narrow down the errors caused by the blown C107 and partially fix them. To decide how to proceed, I still have the following questions:
Is my assumption plausible that the most likely cause of the remaining errors is a damaged STM32?
Is it likely that the 9.5 kilohm resistance between ADC_3V3 and GND could cause overvoltage at VDD and cause further defects?
If so, is it possible to obtain programmed STM32s? I have already received offers to replace the STM32, but programmed STM32s are not available. Without these, a complete repair would probably be impossible.
I am aware that such diagnoses are difficult to make via a community forum. That is why I created a support ticket a week ago. I did not expect a solution, but at least some suggestions for further troubleshooting. Unfortunately, I have not yet received a response. I find that a bit disappointing. It takes a considerable amount of effort to understand the complex technology of the QMX and analyze errors. The results are certainly also of interest for the further development of the QMX. I would appreciate some support from QRPLabs, even though this is primarily a community-supported project.