Refer: Possible to make/save Librem 5 distro + data as an image file? - #51 by irvinewade
(I can assure you that Ubuntu 22.04 regular boot, not live boot, does work fine with the Librem 5 for reflash or Jumpdrive, for example. Even with a live boot, you will get there in the end.)
I probably have a deficit of information regarding your exact environment … but … my suggestion would be to use a separate portable drive attached to the host computer (can be a flash drive if that’s all you have or, yes, even an SD card if that’s all you have), with the only requirement being that it needs to be able to hold an image of the source phone’s eMMC drive (about 32 GB).
So you probably need an approx. 32 GB drive for the live boot and an approx. 64 GB drive for the source phone’s eMMC drive image.
If you are super-desperate … dd piped through gzip would reduce the disk space requirement on the host computer for holding the disk image. (That’s what I do for holding my Librem 5 backups on the host computer. The only disadvantage is that then you can’t directly look at any files inside the backup from the host computer.)
I can’t really comment much on what gnome-disks might be trying to do. Perhaps it is trying to use/tmp for something.
I think the live boot environment uses overlayfs (or something equivalent to that) in order to allow you to make temporary modifications to the read-only live boot. (That’s why sudo apt install something works at all in the live boot environment.) I have no idea how much disk space it allocates for that but clearly it is not an unlimited amount of space and multi-GB files may just be too much.
If you really get stuck, you can always install Ubuntu from the live boot to a portable drive (of any type) and then boot the portable drive. In that case the single portable drive needs to have enough space for Ubuntu plus the disk image.