Pages file "is damaged and can't be opened" - any recourse?

The only recourse is an earlier version of that document that you have backed up on Time Machine, and can restore. Or an earlier version of the document that exists elsewhere.

Once a Pages document is damaged, you are done with it. This is far less likely to occur if the Pages document remains on your Mac startup drive, iCloud Drive, or USB attached storage. Non-Apple cloud services are no guarantee against Pages document damage.