For those finding this again on Google, the solution was:
Using DiskInternals Linux Reader to access the Linux partitions on a Windows machine. I found a partition with the directory (I know this looks odd, but directly copied from DiskInternals software) “/var/log/journal\supervisor\backup”. It has a lot of tar files that appear to match the “slug” values I saw in the HomeAssistant CLI, so I’m sure these are the backups I made.
I can confirm that inside one of the large tar files I found are the following files:
./backup.json
./homeassistant.tar.gz
Unpacking the archive I found all my configuration yml files and a copy of my database. Success!
To unpack a tar into the current directory:
tar -xf homeassistant.tar.gz