This is possible in Linux using v4l2loopback and gphoto2.
I use my Sony a7r II as a webcam on Linux using gphoto2 with v4l2loopback:
https://daniel.lawrence.lu/blog/y2020m03d31/
sudo modprobe v4l2loopback devices=1 exclusive_caps=1 card_label="pupcam"
gphoto2 --stdout --capture-movie | ffmpeg -i - -vcodec rawvideo -pix_fmt yuv420p -f v4l2 /dev/video0