Can’t restore MacOS from recovery
This is pretty easy if you have a network that works or a second Mac.
I’m not sure you have either based on the initial version of your question. You may have both based on the edit.
The erase install process works great for us on the hardware you have. I wouldn't mess with bootable media if you can download from Internet Recovery.
Instead - erase the disk, which returns you to the Catalina installer. While it's running - look for Command-L and Command-3 to show the log file and show all logs.

Since you’re between versions: - https://support.apple.com/en-us/HT204904 -  use Shift - Option - Command - R.
This is the most reliable erase process: - https://support.apple.com/en-us/HT208496
This is the most reliable recovery process: - https://support.apple.com/guide/apple-configurator-2/revive-or-restore-mac-firmware-apdebea5be51/mac

It's unlikely you need Apple Configurator, but know you can bypass everything and start by restoring the T2 chip and then write a new BridgeOS if needed on T2 Macs.