How do I retrieve Pages and Numbers on Mac with macOS Ventura 13.7.5 after battery replacement?

If you launched the Mac App Store and signed in with the same Apple ID that you used to originally install Pages and Numbers, and then pressed cmd+0 (zero) to open the Purchased panel, then you should see entries for Pages and Numbers there.

The exception to the first paragraph is if Pages and Numbers came preinstalled on that Mac, whether by Apple, a third-party reseller, or a previous owner. Although you may have updated these applications, you were not the original installer and they will not appear in your Purchased panel. There will be no means to obtain these applications for Ventura 13.7.5 now.

Open the App Store, check App Store > Store > Account. Your previous downloads of Pages and Numbers should be there for download.

Not sure why a battery replacement would have hosed anything on the local drive... Sounds like that's not all they did.

+1

Restore them from your backup.

You do have a backup of your Mac, right?