You can't install an .iso to a partition, it requires writing to the entire block device.

ventoy would work for you. After setting up the USB stick you can just drag and drop .iso onto the thumb drive. When you boot from that thumb drive all the .iso on the drive are presented in a boot menu.

ventoy isn't available in Debian but you can find a .deb here or you can get the official .tar.gz from ventoy's github page

My own ventoy stick has systemrescuecd, a bullseye netinstall image with firmware and a Debian mini-iso. Check ventoy out - I think it might be just what you need.

cheers -