Since I don't have the same equipment, I can only give a limited answer. I tested it with an iPhone 11 and Logitech G935. You can listen to music, but I can't say whether the microphone works. I couldn't make a phone call because I couldn't switch to the headphones, only the normal hands-free system worked.
A Jabra with a cable didn't work either because it draws more current than the adapter allows.
What works in terms of microphone is, for example, the S6D uTestMic. This is a calibrated USB microphone that can be operated with this adapter. It has a microphone and a headphone output at the same time. But it's not meant for making phone calls. I don't know if all this will help you. You probably have to try it out.