Question about B&O Beoplay H4

You can connect perfectly to the computer and choose the microphone you have in the audio options. At least in macOS, in Windows I don't know.

Microphone does not work on the PC via cable (with integrated microphone). What can I do?

Well, Windows (still) has a bit of a hard time with Bluetooth accessories. It works, but can cause problems when reconnecting or similar. Traditional (USB or 3.5mm jack) headsets work better in my opinion. However, these headsets are not very suitable for video chats or phone calls; if the volume is too high, the other person will hear him/herself (due to the lack of passive noise isolation of the headphones). In addition, the microphone is not in front of the mouth, which could cause problems in noisy environments. I would rather choose office headsets for the PC and these for music or film enjoyment, because the sound is quite convincing.