Is there a way in postgres or using some other tool to allow for a privileged user (admin) to have necessary privileges for administrative functions but not be able to actually query sensitive data?
The only means it has is encryption. And not on the database side, but on the application side before the data is stored in the database.
This is the same problem as when you use some cloud storage. How do you prevent, for example, Google from spying on the data you enter in Google Drive?