MBP M3 Migration complete, but Photos: cannnot find anything via album, keywords, date, title, obvious shapes....

I'm surprised it didn't work. But you can certainly restore from a Time Machine backup. All the pictures and data are stored in the Photos Library in the Pictures folder. You need to protect your original Library -- drag it to another folder, maybe Documents, so that restoring from TM doesn't overwrite the original. Did you have "Optimize Mac Storage" turned in in the iCloud settings? If so, the Time Machine backup may not have full sized images, but that should be OK.

Restoring from iCloud will also work, but it will take maybe a week or more to finish. You can make a new, empty Photos Library, make it the System Library, and turn on iCloud in settings, and Photos will fill the new Library with the pictures in iCloud. It is fastest when you're not actually using Photos, so just leave the computer plugged in and running all night, but have Photos in the background-- have a Finder window in front.