Can't get Fujifilm Webcam software to work with X-S10

First, I'm happy to help. This isn't a problem I currently have but I can easily see it becoming one.

Agreed. It's still a mystery and I share your observations about why it "should" work. I think the camera will try to charge whenever it's connected to a power supply — I get the little "AC plug" charging icon on the display myself. Of course, this doesn't guarantee the battery is in fact charging, that supply is meeting demand,  only that power is flowing into the battery.

My questions are:

1) Are we certain that the others who have this working are using an X-S10? Beyond that, we can't discount the possibility that this is in fact a "Mac thing" but I'm hard-pressed to see how this would be a factor. Some sort of " battery handshake" that the Mac requires and the PC doesn't?

2) Are we sure that the power supply in your particular adaptor is "up to snuff" and provides the rated current. (I have some ways that I might try to measure this but I'm not comfortable advocating or sharing them — you either know how to test it, and are comfortable doing so, or you're aren't — and probably shouldn't.) Besides…

I feel we're getting off into the weeds. The goal here is a webcam that works for you in what seems to be a business application, not satisfying my intellectual curiosity. (But I am curious, so if anyone has anything to add…)

To that end, you should either learn to live with the compromise of batteries, explore alternative means of connecting the X-S10 (HDMI capture adapter — mine was $18 plus an HDMI Micro - HDMI cable and OBS Studio's Virtual Camera — which adds complexity) or forget the Fuji and get another webcam. FWIW, I seldom use either of my Fuji's for this. When "presenting", I connect my iPhone's back camera via NeuralCam Live. If I'm not a "primary participant" I live with the camera on the MacBook. (Or use my iPad — but that's another kettle of fish.)

Good luck!