MGboston

Thanks @CatsAreGods I had somehow ignored or missed this very explicit reference in the manual that answers the question. However, the answer to "why doesn't the USB power connection eliminate any battery drain?"  remains a mystery. I think this model and the switch to USB-C was not as well engineered as we'd expect from a company like Fujifilm. 

Thanks @CatsAreGods. The thing that is confusing to me is even when the "plugged in" icon is showing why is the battery draining to the point where the camera shuts down?  I am fine if the battery can't charge (e.g. move from 2 bars to 4 bars), but I didn't think it ever ran down before. Can you confirm if your battery drains while it's plugged in? 
My working hypothesis/ conspiracy theory is that the camera's ability to pull power from the USB port is not sufficient to off-set its full draw. When I was using USB and XWebcam2, perhaps the settings downgrade the performance to work around this issue. However, now that I am using the HDMI capture card, it's demanding more power, thus losing charge. Maybe the S-X10 and the XT30 share a battery/ power supply design, then maybe it makes sense why they're the two recent models that don't have full support for XWebcam2? Which would then answer the ongoing question in this forum of "is Fuji making this decision based on hardware limitations or marketing strategy?" -- Fuji has an antiquated battery/ power management design that it probably didn't realize would hobble webcam usage. Anyway....it's a theory that might be wildly wrong. 

Thanks to @Joe Roxx, @0301chris, and @flamidey for the guidance on capture cards. And fingers crossed that the X-S10 gets full Xwebcam2 support, but given that we don't know when or if that will happen and what the resulting quality will be...I decided to experiment on the cheap ($26 total) with: 
Micro HDMI to HDMI Adapter Cable, Wenter 6.5ft/2M Micro HDMI to HDMI Cable (Male to Male) for Gopro Hero and Other Action Camera/Cam with 4K/3D Supported Video Capture Card, GUERMOK USB 3.0 HD Audio Capture Card, 4K 1080P60 Capture Devices for Gaming Live Streaming Video Recorder, Compatible with Windows Mac OS System YouTube for PS4, Switch, Xbox So far so good. It's the same level of control (everything set up on the camera), but with a much better image (full frame rate). Wishing I had pulled the trigger on this from day one.

Thanks to @Joe Roxx, @0301chris, and @flamidey for the guidance on capture cards. And fingers crossed that the X-S10 gets full Xwebcam2 support, but given that we don't know when or if that will happen and what the resulting quality will be...I decided to experiment on the cheap ($26 total) with: 
Micro HDMI to HDMI Adapter Cable, Wenter 6.5ft/2M Micro HDMI to HDMI Cable (Male to Male) for Gopro Hero and Other Action Camera/Cam with 4K/3D Supported Video Capture Card, GUERMOK USB 3.0 HD Audio Capture Card, 4K 1080P60 Capture Devices for Gaming Live Streaming Video Recorder, Compatible with Windows Mac OS System YouTube for PS4, Switch, Xbox So far so good. It's the same level of control (everything set up on the camera), but with a much better image (full frame rate). Wishing I had pulled the trigger on this from day one.

Thanks to @Joe Roxx, @0301chris, and @flamidey for the guidance on capture cards. And fingers crossed that the X-S10 gets full Xwebcam2 support, but given that we don't know when or if that will happen and what the resulting quality will be...I decided to experiment on the cheap ($26 total) with: 
Micro HDMI to HDMI Adapter Cable, Wenter 6.5ft/2M Micro HDMI to HDMI Cable (Male to Male) for Gopro Hero and Other Action Camera/Cam with 4K/3D Supported Video Capture Card, GUERMOK USB 3.0 HD Audio Capture Card, 4K 1080P60 Capture Devices for Gaming Live Streaming Video Recorder, Compatible with Windows Mac OS System YouTube for PS4, Switch, Xbox So far so good. It's the same level of control (everything set up on the camera), but with a much better image (full frame rate). Wishing I had pulled the trigger on this from day one.