Trying to reinstall Ubuntu on an external NVME drive but getting error when booting - Alert! uuid does not exist. Dropping to a shell!

You have installed grub twice to drive shown as sdb. And have /EFI/ubuntu in the NVMe drive. Only one is updated with reinstall. Only one of those should work. Review entries in UEFI boot menu. Report does not show any UEFI entries for ubuntu nor UEFI:external drive's label. Also external drives lose UEFI entry when disconnected. Then you boot external just like live installer choosing the UEFI:external drive entry which then must be updated to work. I would set that is default for grub updates in fstab.

Once in BIOS boot mode as you have grub in gpt's protective MBR and a bios_grub partition and you have an ESP with /EFI/ubuntu & /EFI/Boot folders. Both of those you would have to select from UEFI boot menu just as you boot live installer. The Ubuntu entry in UEFI is from the ESP on the NVMe drive. With 3 grub installs you have a 1/3 chance of selecting the correct one.

How you boot install media, UEFI or BIOS is then how it installs or Repairs. So you want to always boot in same boot mode.

External drives only directly boot in UEFI mode from /EFI/Bootx64.efi just like how you boot installer. The ubuntu entry in UEFI would be from NVMe drive's grub. And UEFI should show a BIOS boot entry.

If always booting external drive from "ubuntu" entry in UEFI, that would be version in internal drive's ESP. You can use Boot-Repair's advanced mode to choose an install and then choose drive to install grub. If you disconnect external drive, this entry will probably stop working. Then you need a valid entry on external drive.

And/or if you want to be able to boot external drive from other systems, you need current grub in external drive's ESP. Again you can use Boot-Repair. I would just be sure to not use BIOS mode to boot, so that grub is never used.

If for some reason you have an old BIOS system and want external to boot it, you can reinstall grub's BIOS version grub-pc and install that. Its just that only one version is updated with reinstall or major update of grub & then they may get out of sync.

Otherwise always boot in UEFI boot mode to make repairs or updates. You will need to review /EFI/ubuntu/grub.cfg, fstab and UUID and GUID/partUUID of UEFI boot entry & partUUID of UEFI boot entry to know which system is default boot and if it has correct entries. Boot-Repair shows all those or:

cat /EFI/ubuntu/grub.cfg
cat /etc/fstab
lsblk -e 7 -o name,fstype,size,fsused,label,partlabel,mountpoint,uuid,partuuid
sudo efibootmgr -v