The AGPL (Affero General Public License) is a strong copyleft license that requires the source code of any modified version of the software to be distributed under the same license terms.
In this case, since there are no modifications the Ghostscript software and are only using it as a command-line tool, the use of Ghostscript does not trigger the AGPL requirements to distribute the source code of your application.
However, it is worth noting that the AGPL does have a broader definition of distribution than other open source licenses. According to the AGPL, distribution also includes making the software available over a network, which means that if you were to make your web app publicly accessible over the internet, then you would be required to make the source code of your application available under the same AGPL terms.
Since you mentioned that your web app will only be accessible internally within your organization, and not publicly available over the internet, your use of Ghostscript in this context should not trigger any AGPL requirements.