My backups were made using Time Machine, and I've been able to successfully restore everything from there! Here's where I found everything that had gone missing:
Users > "username" > Library > Containers > com.seriflabs.affinitypublisher > Data > Library > Application Support > User
Inside that folder, the assets.propcol file is what I restored for my missing assets. I also had to restore my macros.propcol, doc_spread_presets.propcol and object styles.propcol files as all of my previously saved macros, document presets, and styles were missing.
In case it makes a difference, my affinity apps were all purchased through the Mac App Store. Hope this helps!