In the future, you should look into using LVMs for your partitions. I ran into a similar problem recently where my /var needed to be increased - I was able to run a simple lvextend -L+4G /dev/myvg/var --resizefs to grow my /var by 4 gigabytes.

Before I was using LVMs though I used a gparted live disk a lot

(I assume you meant “I created a separated /var partition”)

You can move/resize partitions from basically any live usb (via cli or gparted for gnome and kde partition manager for kde).

Shall you want to, you can also merge the var partition with (say) your root partition:

1. mount both partitions in two directories (just create empty ones and mount on them, say ~/root and ~/var)
2. inside ~/root create the new var/ directory
3. copy the data over
4. edit ~/root/etc/fstab (remove the live for the old var partition)
5. use whatever partitioning tool to get rid of the actual partition and expand the previous/next one

Be aware that you can very easily lose your data ;)

PS: just in case, try running flatpak uninstall --unused

Is there a reason you gave /var it’s own partition? Or is the problem that your entire root file system is full?

As others have said if you have a /var partition, resizing should fix the problem but the other solution would be to migrate the contents back to your main file system partition. Presumably at present there is a symbolic link folder pointing to your /var partition? Copy the /var partition contents into a new folder then boot in to recovery mode and delete the symbolic link and rename the new folder to /var. However presumably you have a good reason for splitting /var out.

If you don’t have a separate partition then the issue may be your root system itself is full and that partition needs resizing if possible or cleaning our to make space.

Finally, Flatpak does also use the /var directories in the home users folders (it uses this for single user installs of software vs system wide installs). It’s possible it’s axtually the home folder/partition that is full and that needs resizing or cleaning out to make space .

Assuming your /var is in a separate partition, you could resize it using a tool like gparted. But make a backup beforehand.

you could move the flatpak stuff onto another partition with same permissions and bind mount it to the original location, then persist it with a line in fstab

Sounds like you created a seperate partition for /var. Only way to change that is to redo your partitions or bind mount an external disk as /var.