I got it working by doing what other's did to fix this: Downgrading the Microsoft LibUSB driver from 10.xxx to 6.xxx using Zadig. OpenOCD is now able to connect to the ESP32-C3 and read JTAG data.

I don't know why it works and that makes me uncomfortable. There could be a bug in OpenOCD or perhaps LibUSB lost functionality.

I was resistant to this fix for a couple reasons. In general, newer driver versions do everything their predecessors did with fewer bugs. I've also had serious problems show up after Windows updates in systems running old, version-mismatched drivers.