The LiveUSB session is a loaded SquashFS. You can normally update and upgrade non-system pacakges (even Core desktop packages that are updated in the repository), but will not be able to upgrade the kernel or boot specific files; due to this.
No, it is not persistent. But it was always possible to run sudo apt update && sudo apt upgrade to be able to install an app like extension manager or today I wanted to install another browser for testing the pwa apps.
I did not change the kernel.
Hmmm
You are right - running sudo apt update && sudo apt upgrade on the live session should still work.
But if a current package in the Zorin Repo's contain metadata in transition; if something is calling update-initramfs, maybe a firmware update or linux base package, then this can happen (It's still SquashFS).
I do not think your USB stick is broken or anything. If this is repeatable on the non-persistent session on repeat boots - definitely is a package in the repo.
Thank you very much, that was a good idea and worked. I marked to hold all kernel updates and the linux firmware, now the upgrade was successul and I'm able to download packages.