Little update, your identification was right, thanks again for that. But it turned out to be the MCU that was bad. Fortunately I know someone with exactly the same model oven and I was able to get the firmware from it. What's interesting though, is that the power supply is set to around 5.5V, which is the maximum operating voltage of the MCU for 5V. The absolute maximum rating is 5.8V. I couldn't find any reason to do that instead of just setting it to the nominal 5V. Maybe for planned obsolescence?! When I replace the MCU I am going to replace the resistors to set the power supply to 5V.
For anyone facing the same problem with their Siemens HB676GBS1/99 oven, I hope you find this post. I'll put a couple of keywords in so hopefully the search engine spits it out if you are searching for: Siemens oven HB676GBS1/99 firmware repair control board 11052160 11038199 MCU microcontroller software NXP MKE14Z256VLH7 programming
If you need the firmware you can contact me at sebastian.salmhofer@custom-tek.com, I will send it to you and also give you the pinout of the connector on the board. I just used a FRDM-KL46Z development board that I had lying around as a programmer with USBDM.
https://usbdm.sourceforge.io/USBDM_V4.12/Freedom/html/freedom_setup.html#FreedomFirmwareInstallation. You can get programmers for around 15 USD if you don't have one. Absolutely makes sense to fix it if you can, Siemens wants over 200 Euros for that damn board.
I'll give you another little update if it actually worked, I have to wait for the Chip now which will take like 2 weeks to get it to Paraguay.