Another possible solution is to use Ventoy. Directly from the tool description:
Ventoy is an open source tool to create bootable USB drive for ISO/WIM/IMG/VHD(x)/EFI files.
With ventoy, you don't need to format the disk over and over, you just need to copy the image files to the USB drive and boot it. You can copy many iso files at a time and ventoy will ...
Simple Hand Made Persistent USB
If you like learning experiences, you can create a multi partition, persistent USB that can install Ubuntu, from scratch.
Boot Installed Ubuntu or Live USB.
Insert Target USB.
Create a GPT partition table on Target USB.
Create a 1MB BIOS boot partition on the left, formatted as unformatted.
Add a 300MB FAT32 ...
Partition the pendrive as you like, giving space for the ISO image in a FAT partition, the first one.
Run lsblk to identify which device is your pendrive, i.e /dev/sdb, being the first partition the FAT one, i.e /dev/sdb1. Mount it, i.e /media/user/PENDRIVE
Mark this partition as bootable, you can do this from Disks utility.
Run these commands:
Shutdown Ubuntu running a live session from the USB by clicking the ⏻ icon in the upper right corner of the desktop. From the ⏻ menu select Poweroff / Log Out -> Poweroff -> In the Poweroff window that pops up click Poweroff button. Shutting down the USB Ubuntu live session will also power off the computer. Then you can safely remove the Ubuntu live ...
In this image, you can see that the grub only recognizes my ubuntu partition
Grub only knows about boot devices with bootable operating systems that it's been told about. Booting from the USB device is a function of your machine's BIOS. Normally this is done with a key press on boot but it varies between machines. It might be Esc, Del, F2, F8, F10, F12 or ...
I'm having a similar problem on Ubuntu 20.04. It seems that recently a bug was introduced in GNOME that causes this, it's being investigated in https://gitlab.gnome.org/GNOME/gnome-shell/-/issues/3299.
If you're using GNOME, I'm positive that your issues are caused by this bug as well.
A quick workaround is to restart the shell after plugging in the external ...