I promised the dd commands although we can see that /var/log had a lot in from the screenshots.
If you have mounted the card using a USB sd card reader the first thing we need to find are the devices:
type 'df' and you'll get a report of the disk file system usage.
You are looking for something like /dev/sdb1 in the first column and /media/username/boot in the last column - that's the boot partition - and there'll be another /dev/sdb2 with /media/username/rootfs - that's the root partition. N.B. username is whatever you are logged in as, if you are using a Pi it will be /media/pi/boot.
If you've mounted them in an mmc slot in a laptop as I have just done, the devices are /dev/mmcblk0p1 for the boot and /dev/mmcblk0p2 for the rootfs. Its outside this post to explain the difference as its deep into Linux devices and naming, but if you eject the card, the devices disappear.
So lets work with /dev/sdb1 and /dev/sdb2 as examples.
To unmount the partitions without ejecting the card type 'sudo umount /dev/sdb1' then 'sudo umount /dev/sdb2' . This means the device 'file' is still there and its this that you use in the dd command.
Assuming the machine you are using has plenty of disk space you can just create images of each sd card partition doing this:
sudo dd if=/dev/sdb1 of=~/boot.img
sudo dd if=/dev/sdb2 of=~/rootfs.img
'if' means input file and 'of' means output file
The boot image copy won't take very long
The rootfs copy will take much longer because the partition is 8GB - or 16GB, or however big the partition is.
Those .img files are now on your home directory, that's what ~/ means along with the filename.
If you create a new bigger sd card with octopi on, you can then copy those image files back.
Put the new card in, unmount the partitions and then use
'sudo dd if=~/boot.img of=/dev/sdb1'
'sudo dd if=~/rootfs.img of=/dev/sdb2'
BE VERY CAREFUL that you know which devices your old memory card mounts on - you don't want to overwrite the system you are running. Once you've copied your image files back over to the new card, eject and put into your Pi and boot - n.b. this won't work if your original images don't have the correct boot files for the Pi you are using, so beware if you are using a card that was created before the Pi4 was released.
BTW, the image files on your hard disk are essentially backups, very useful, I've just had a Pi trash its microSD card and I've had to rebuild Octoprint on a new one.