They did make the "Imaging Edge Webcam" program, I think some time during the pandemic, but AFAIK it's just a PTP preview to webcam driver, so the quality is pretty terrible and you can do that with OBS+gphoto2.
My older Sony cameras (A6300 is my newest "old" Sony camera) don't have the feature (unless you use that terrible software you mentioned) Im surprised to read that even the reasonably modern A7SIII doesn't support it. It must be one of the last models without USB streaming support.
For older cameras, probably the easiest way to do it (if you don't want to install anything) is to pick up a ~$20 usb HDMI capture card from amazon. Connect the HDMI output on the camera to the capture card. And then set your camera up to output a "clean" video source via the HDMI port.
As I understand it, modern capture cards work without drivers on every OS, just like the modern sony cameras do.