Here is what works for me, on my X-S20: Before connecting the USB cable, put the vamera in Vlog mode and select Auto Power Off to "OFF" in the Power Settings menu. Then turn off the camera, connect the USB cable, and turn it on. I am using the Fujifilm X webcam driver that can be downloaded from https://www.fujifilm-x.com/products/software.
Note that putting the camera in any other mode than Vlog, or setting Auto Power Off to anything other than OFF, will cause the camera to power off automatically after a while. This is a more than questionable design choice for Fuji - not to call it a bug - as nobody in their right mind would expect a webcam to automatically power off while being used.
Remember to set Auto Power Off back to your favorite choice once you are done using it as a webcam.
Another thing to keep in mind is that the camera seems to be drawing power from its battery, rather than the USB port, while being used as a webcam. This is not documented in the owner's manual. So I strongly recommend you use a dummy battery with an AC adapter instead of the battery.
