Granting read and write permission to the disk is not the same as grating read and write permission to the FOLDER where you are trying to export the photos to. You have to set the folder to write permission. Or choose a different folder where you already have write permission.
I indeed have set full permission to the disk on the "Total access to disk" section of the security and privacy settings.
The other section, "files and folders", that I think you mean, does not give me the option to change anything, if the previous setting is full permission. The only way to grant access to folders here would be to deselect total disk access on the previous folder. In that case, the options appear: external disk, download folder, documents folder, etc.