So after more testing and some time trying it on the trainer, I thought to get at least one thing going and built a board to fit the STM and the power supply for the servo.
Here you see me riding my bike on the trainer and my high sophisticated test setup:
The breadboard clamped to the trainer with a spring clamp.
After I found everything working ok I soldered the board together,... also highly sophisticated (without any plans and I think it was 01:00 am). Next time I should plan ahead, it will definitely save me some time and headache.
Again some testing and I must say: I feel safer already knowing my trusty rubber band will hold everything in place....