The disks I'm listing are original OS 2.04 disks from an Amiga 2500. I think the only difference between OS 2.0 and 2.04 is just a few bug fixes. Almost all the OS2 disks out there are 2.04. The next major upgrade was OS2.1. That would also be compatible with your system. You would need a 3.1 rom if you wanted to install OS3.1 or later.
Amigas are a lot simpler and more tolerant and flexible than PCs. If you had copied all the files in your system partition to a folder on another partition, you could simply boot from a floppy and delete the corrupt files on your system partition and drag and copy the files from the backup folder to your system partition and reboot and everything would be as before. This is my Amiga backup system.