Automatically hide mouse when typing

The default macOS behaviour is to hide the mouse when typing. I often find my recordings have the mouse obscuring what I am typing because the cursor has been hidden on the screen I am recording.

There is a very manual option to do this by exporting out two versions of the recording - one with mouse, one without - and choosing which one to display when editing in DaVinci Resolve, but since the cursor automatically hiding when typing is my preference, I have started using another piece of screen recording software to capture the expected system behaviour.