I got an answer from the support.
Perhaps I should say that I decided to report the issue to the support because I started to hear this noise even after a bluetooth connection was established. I noticed it for several minutes after power on, and even during music playback it was audible.
The support recommended me to do a factory reset (slide and hold the power button to its upper position for 10 seconds). This would clear all saved bluetooth connections. After that I had to do the pairing again.
This definitly improved my situation. Now the high frequency sound is only audible for a very short period after power on.
I should add that I had muliple bluetooth devices paired with the headphones (at least four). After the reset I have only paired one device so far.
So my conclusion is that the noise is correlated to the headphones scanning for a special (maybe the preferred?) bluetooth device. If the device is found or a timeout occurs the hissing sound stops.
The support also recommended to first power on the headphones and then wait until the signal LED turns off before putting them on. This would ensure that the proximity sensor can be calibrated. This has nothing to do with the high frequency noise (as far as I know), but at the time when the signal LED turns off, now the noise already has stopped.
Other than that the support neither confirmed nor denied that this issue is special to my pair of headphones, if all H9i are affected, or if this is a known problem at all.
I will see how this develops once I haved paired more than one device again.
Greetings