MacBook Air file system seems to have disappeared

My 13” MacBook Air (2012 or 2013 model) with a 500 GB SSD hung the other day and when I rebooted, it came up in Mac OSX Utilities, apparently from the Recovery Partition (wherever that is). It offered to recover from my Time Machine, but could never find a disk to recover to. Similarly, Disk Utilities also couldn’t find a disk to repair.

I did the R boot and got the same Utilities program with the same results (no disk).

I made a bootable OS (Mojave) Install drive to boot from, but again could not find a disk to install to.

My IT friend suggested that the SSD was dead and I might try replacing it. For ~$250 I can put in a 1TB SSD it appears. But if it doesn’t work I have a $250 SSD and a dead computer, so I thought I’d ask here if there is any way I can explore further or if it sounds like the SSD Is really the culprit.

Thanks!