@zontex Hello, i am happy to tell you that i was able to solve the problem :-)
One of my Hats has a defect LED and the code I used to test the other one was based on wrong assumptions.
I simply set the RGB to 0xFFFFFF. But because the coprocessor on the servo-hat reminds the last active value, even after a power off, it never switched on the Led as long as I used the same value again and again. Changing the color of the RGB in a loop suddenly switched it on. Using the same code on the other Hat revealed that this one has a broken LED. Mystery solved!
Thanks for your help so far and best regards
@m5stack I think it would be a good idea to change the code of the 8servo hat, so that on power on, the LED is initialized with the stored values and not simply left off.