Using second monitor when also air playing
I am an educator with the following setup: I have a projector that I have set up as a second monitor to my MacBook air. I want to be able to control my presentations through an iPad (and apple pencil) and have found that I really have to use airplay to have it displayed (no more doceri). When I airplay the iPad to the MacBook, I can predict the iPad's mirror, but the screen on the macbook is black. Is there a way to have it still work as a screen for the MacBook (so I can use it to take role, check other resources, etc.)?
iPad is 8th generation and macbook air is a 2020 M1.
MacBook Air (M1, 2020)