Solutions
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wblondel's post in Cannot commission Matter over Thread devices using phone connected to Home Assistant VM was marked as the answerAlright, so after trying to make the commissioning work with other routers configured as a media bridge (which failed), I bought a pair of CPL. I connected one to my ISP box downstairs, and one to the Ethernet port of my NAS. Then I passed through the Ethernet NIC to the Home Assistant VM and configured the VM so that it uses only this NIC.
It now works flawlessly.