With new Network install (beta) Network install beta test: your help required! - Raspberry Pi method, I think we will no longer need a computer to install HA on raspberry pi. I don’t have the hardware with me right now (waiting for the adapter to ship). If anyone could confirm that we no longer need the SD card after the initial upgrade to the beta bootloader.
In theory, if RPi 4 is running beta bootloader, we will simply connect the SSD with the relevant adapter and install Homeassistant from Network install Raspberry Pi Imager.
Raspberry Pi does what Microsoft can't! - YouTube