Mac HD [Big Sur] not showing in Catalina Installer via Recovery or Bootable USB Drive

Created a bootable installer drive on an external Samsung T7 drive connected via Thunderbolt 3 cable. Partitioned the drives with 3 OS installers: Mojave, Catalina, Big Sur.

Machine (2019 Maxed out MBP) currently has Big Sur installed.

The bootable SSD shows up in startup drives and the Catalina install process proceeds correctly until prompted to "select the disk where you want to install MacOS". The only drives listed are the drive/partitions on the external SSD. The internal Mac HD is not an option.

Thoughts?

Thanks!