RonR-RPi-image-utils VS PiShrink

You could try something like image-backup. This can create an image from a running Pi. If you don't care about backing it up while running you can use one of these options

Unofficial Github

Image-Backup is one module of Image-Utils and just like borgbackup is simply a script, not available with apt-get. Just copy the script to your /usr/local/bin folder and make it an executable. It looks like it is being maintained at: https://github.com/seamusdemora/RonR-RPi-image-utils .

There is a small utility, which shrinks the image by omitting the empty space. Then you can write it to any SD card, which the data will fit on. So in your case even on a 2GB card.

backup.sh - this is what makes the image and uses pishrink to shrink it

Depending on what single board computer you are using, you may want to look at PiShrink. This will at least allow you retroactively shrink the image you create to the actual amount of space used.

I was pretty familiar with most of this but I did not know about the "image backup" utility. You may also want to look at PiShrink in your process as well.

I run a full dd to create an image and then run pishrink https://github.com/Drewsif/PiShrink on it. I used to manually size the partition down with gparted and calculate how much to dd and then gparted the new card to expand the partition - too much work. Pishrink does all the work for you and is fast.