Applications(iWork) won’t open after downgrading from Ventura to Monterey
Except for the system version, the issue and condition are same as Applications won’t open after downgrading - Apple Community.
On my end, it was solved by completely removing the app (Number, keynote and Page) based on https://macpaw.com/how-to/uninstall-apps-on-mac-os-x.
After restart the OS, the Number, keynote and Page can be opened
Mac mini, macOS 12.6