Hi,
I tested again, but it seems to be all right on our ends regarding the “school” custom field: https://i.imgur.com/DR1nWvF.png
The partners field values are requested from ACF directly. It is possible, that the ones, which may not have any posts assigned to them may not be returned by ACF yet.
Another possibility is that ACF simply does not return those choices. It is notoriously hard to get object storage field values correctly via using their API, it is known to them as well.
If you want, you can add temporary FTP details, and I will try to go through the relevant code, to see if there is any way to get the missing elements somehow programmatically.