How install latest mac os (Bug Sur) from recovery mode?

I need to reinstall the macOS to MacBook pro-2015 13-inch. I erased my disk and try to install the latest mac os from recovery mode. It's installing Catalina. How to install Big Sur from recovery mode? Is both OS store in the disk If I install Catalina and then upgrade Big Sur from system update? is it possible to install Big Sur from recovery mode in the below way?

Now, I'll install Catalina from recovery mode, then I upgrade to Big Sur from System Update. Then I clean the disk again from recovery mode and try to reinstall os from recovery mode?

I need to save my disk space. because my disk space is 128GB.