That's truly frustrating, and I'm sorry to hear about your lost work! Losing unsaved progress due to an unexpected shutdown is a painful experience.
You're right that Spine's auto-backup system only works for projects that have already been saved at least once to a file location. If a project has never been saved, there is no file for the auto-backup system to copy, so it won't create any backups. This is a known limitation.
Here are a few things to keep in mind going forward to avoid this situation:
Save your project immediately when starting work. As soon as you create a new project, use Cmd+S (or Shift+click the save button in the titlebar to use "Save As") to save it to a location on disk right away. Once the project has a file location, Spine's auto-backup system will kick in and periodically save copies.
Check your backup folder. If you had saved the project at least once before, you may be able to recover a recent version from the backup folder, which on Mac is located at:
<user home folder>/Library/Application Support/Spine/backups
You can also open this folder quickly via the Settings panel in Spine.
Regarding auto-save for new/unsaved projects — this is a great feature request and definitely worth raising. The idea of Spine warning the user or saving a temporary recovery file even for brand-new unsaved projects would be a valuable addition, especially since professional tools like the ones you mentioned handle this gracefully.
Again, I'm sorry for your lost work. Hopefully saving immediately at the start of new projects will help prevent this from happening in the future!