I have noticed that Sony A7R IV and A9 II models do not support live view over the USB 3 connection. Is that just a software feature/compatibility that has not been implemented yet and is in the pipeline?
Both Sony A7R IV and Sony A9II are already supported in Capture One Pro, Capture One Pro (for Sony) and Capture One Enterprise.
IMPORTANT: Update your camera firmware.
For now, live view is possible with the USB 2 cable and the USB-Micro B connector on the camera.
Tethering works with the USB 3 cable and the USB-C connector on the camera.
Also, be sure that the PC Remote function on the camera is enabled. Please refer to your camera's manual.
If the suggestions above have not resolved your tethering or live view issues, consider checking the following articles as well:
Hot Folder option in Capture One (in case your camera is not recognized or supported by Capture One, but you can use the camera's proprietary software for shooting tethered)