Connecting an external Video Camera and Recording onto that camera at the same time.

I use an external Sony FDR-AX700 video camera when I am conducting a Zoom gathering.  I would like to ALSO record with that same camera onto the SD cards loaded into the camera.  However, whenever I push 'record', the Zoom screen goes black. I am wondering:  is there a video setting that allows me to use an external video camera AND also record onto that external camera's SD cards?  I want to use the Camera Recording rather than using Zoom recordings, so that my subject (speaker) fills the screen for the entire presentation rather than just a tiny window on the side (when the presenter goes to shared screen).  Any ideas would be appreciated.  Thank you.