No packages eligible for install?

Ok so I have a late 2012 iMac that I've been running on El Capitan. However, after successfully updating the software on my late 2012 Macbook Air the other day I decided it was time to update the desktop. I knew it was too old to update to Big Sur but I figured a slightly newer software would be better.

Unfortunately, it wouldn't complete the update to Mojave so I tried to restore from my time machine back-up but that wouldn't restore either. Eventually, Apple support had me on Internet Recovery Mode and it offered me Catalina but that wouldn't install either. And this confused me too because support said I'd have to download the software the iMac was shipped with which was definitely NOT Catalina so I'm not surprised it didn't work.

The message that came up was "No packages were eligible for install. Contact the software manufacturer for assistance."

So basically I have an iMac with a completely erased HD that's not letting me install anything. Until yesterday my computer was working just fine. In fact, I think the only thing that wasn't was my mail app but that didn't bother me too much.

Any ideas? I'm thisclose to taking it to a computer repair shop but I'd like to avoid that if possible because money!

Thanks in advance!