Trying to understand the "no space left" issue...
Here is the file size:
When 16.04 is installed, the extracted size ( 1379+181 = 1560 Mo) corresponds to this partition:
df -h
Filesystem Size Used Avail Use% Mounted on
/dev/loop0 2.0G 1.6G 241M 88% /
What I don't understand is why 20.04 installation is failing; while the extracted size (1664+227 = 1891 Mo) should still be inferior to the 2 Go partition size... 
EDIT: I made a trial on my computer. Decompressing both rootfs and device tar.xz on an empty ext4 image file, the used space is 2,041,232 Kb; so more than the phone partition size!
There is not enough free space on the partition to hold the data. The deficit is about 170 MB.