Are you able to save files from any other program to the NAS via the iMac?
The issue of permissions indicated exactly that. It is probably related to hoiw you have your NAS setup. Launch the Control Panel for the NAS in a browser and check over the settings for SMB/AFP/NFS You will need to make sure AFP is enabled.
Next find any folder in the NAS (again from within the browser) and look at the permisions for it. You can have multiple users for the NAS with varying permissions. Make sure the user account use log in to the NAS with has the appropriate permissions.
I am not an expert with Networks but I have been using a Synology NAS for a few years now with zero issues relating to saving a PSD file from Photoshop. I store my images on the NAS, open them directly through PSCC or via Lightroom CC Classic and have no permissions errors.
Thanks for your advice, but the NAS isn't the problem. Everything is filled in correctly. I don't have issues with other files. It's a Photoshop/Mac/Nas issue.