I think I found it -- the files are in AppData\Local\Packages\Microsoft.Windows.Photos_8wekyb3d8bbwe\LocalState, and the catalog appears to be held in an SQLite database therein. Unfortunately, syncing the files didn't work out since it seems that Microsoft Photos keeps running in the background even if it's been "closed", so the files are always locked and cannot be replaced. Even if they could, Photos canonicalizes file paths so if the photo library is on one of the machines then it'll force the local path instead of using the universal network path, and the database won't work on other machines.
