Mac HD seemingly disappeared from Late 2012 iMac. Cannot reinstall macOS! Please help!

Hello all,

This is my first question asked to the Apple Discussions however I'm in a fairly desperate situation. First, a bit of a backstory:

I've been using my Late 2012 iMac for just under 9 years now and have just decided to upgrade due to how slow it has gotten (it uses a 1TB SATA drive). Because I am planning to upgrade, I started to back up my data to an external hard drive. However, I decided not to use Time Machine because I wouldn't have been able to individually select files to back up. I backed up most of my machine to the drive, but while I was exporting my photos library to the external drive, my computer crashed. This was during the export, meaning some photos had gotten backed up - but not all of them. It has crashed in the past and I'd been able to repair the disk through recovery mode and/or reinstall macOS, however this time nothing I did could even launch recovery mode - and Apple support couldn't help either, suggesting I bring the machine in for repair which I did not want to do because I had just purchased a brand new machine.

I was getting the error code -2003F which apparently is related to my network, so I went out and bought an ethernet cable which actually fixed the problem. I was now able to boot the computer into recovery mode, however whenever I tried to use Catalina recovery mode, I would get the spinning rainbow ball on disk utility. So I booted into Mountain Lion recovery mode, which ran fine on my machine. However, when I attempted to reinstall OS X, there was no disk there that I could use.

According to Disk Utility, there is a disk entitled "1 TB APPLE HDD" with a sub-disk "disk1s2." There was another entry entitled "disk0" with a sub-disk "Mac OS X Base System." Repairing or verifying either of these does nothing.

I'm not entirely well-versed on Mac internals and therefore I don't really want to play around with any of this stuff, so I thought I'd come here where the experts hang out. Is there any possible way for me to recover my Mac HD and recover my data? The Apple Support representative didn't seem to think so, but I thought I'd ask here before taking drastic measures. I have included a photo of the current state of disk utility and "reinstall OS X"

I have not partitioned or altered this drive in the past. I haven't been messing around with disk utility or reformatting disks. All I did was export my photos to an external hard drive, and crash.

I appreciate in advance any help I receive. I would be happy to supply more photos/information and try anything you guys suggest. Thanks!