Yes, I will re-setup the system using a SSD.
It might be just a small benefit next to all the trouble you have. But the new install would be Debian Bullseye, while your current one was still Buster. 
We could try to manually replace the corrupted library files, but no guarantee that this will work if the SD card has bad blocks/is dying and we don’t know whether more files are affected. So cleaner would be indeed a fresh image, it that doesn’t cause too much work.
Is there a manual how to install a bootable DietPi on a SSD for Raspberry Pi 3? I couldn’t find anything.
simply flash you image directly into the SSD, similar to how you would do it on a SD card. Keep in mind, all data on the SSD will be removed.
Depending on the exact model, mass storage boot might need to be enabled as well. https://www.raspberrypi.com/documentation/computers/raspberry-pi.html#usb-mass-storage-boot
In case, not all flashing tools list 2.5" USB drives. If you do from Windows, Rufus has an option to show and select them.