This guide explains how to install a full Ubuntu system on an external USB drive or SSD, so you can plug it into any compatible computer and boot into your own Ubuntu desktop, with full persistence and saved settings.
The main challenge on UEFI systems is bootloader isolation: by default the installer may mess with the host system’s ESP (EFI System Partition). The trick is to temporarily hide the host’s ESP from the installer so it instead creates its own ESP directly on the USB.