I was able to finally get Google Photos to back everything up. It's not a perfect solution, but it does seem to work for now.
Uninstall / Reinstall.
I just completely uninstalled the app, then immediately reinstalled it from the Google Play store. One of the first things it asked about in its "first-time setup" procedure was whether or not I wanted it to ...
If the device is rooted you can manually restore the backup.
On a PC extract the backup file using Android Backup extractor.
This will convert the backup to a TAR archive.
(optional) extract the APK files (if the backup contains not only app data) and install them via adb.
Upload the TAR archive to your device via adb push and untar it.
Copy the files you ...
You can use adb backup. You can specify the package name for backup a single app.
adb backup [-f <file>] [-apk|-noapk] [-obb|-noobb] [-shared|-noshared] [-all] [-system|nosystem] [-keyvalue|-nokeyvalue] [<packages...>]
adb restore <file>
Note: some apps won't allow adb backup. even if adb backup is allowed, cache is not included.