How do I record video on my computer using a (mirrorless) camera as the video source?
There are some options, but I am not sure what would work on your specific camera.

If your camera has an HDMI direct output you could use one HDMI to USB converter, one I know that works well is ElGato.

But here is the issue, you need to test if your camera sends a clean HDMI signal, this is without any menu, timestamp, configuration, etc. Test this connecting the camera to any TV.

Another thing to consider is the time the camera remains transmitting, for example, if it is not recording. It could just turn off in the middle of the transmission.

You can also try a tethered software that can use live view mode. The problem here is that the camera will transmit a Still Image size, for example, an 6000x4000, so the the result could be at an extremely low frame rate.