Recover data in Sparsebundle disk Image
Well, I'm in luck.  I wandered around google drive, and right-click on the relevant folder showed me activity in March.  And, strangely, 14 of the band files had been deleted. Google drive had an option to restore them, individually.  After that downloading the whole sparse bundle as a .zip file, and expanding it, the bundle is now recognized again.

I think the file deletions happened when I was messing around with google drive settings, changing it from "Ask before deleting everywhere" to "Remove items everywhere", on a computer that was sync-ing a much smaller subset of directories.

Lesson, (a) don't depend on Google for anything (although in fairness Drive did provide the tools to recover), (b) for important things, have multiple backups