If I understand correctly what you say, this is one of the main concerns with the SSPL because of the following [1]:
> The SSPL is based on the GNU Affero General Public License (AGPL), with a modified Section 13 that requires that those making SSPL-licensed software available to third-parties (modified or not) as part of a "service" must release the source code for the entirety of the service, including without limitation all "management software, user interfaces, application program interfaces, automation software, monitoring software, backup software, storage software and hosting software, all such that a user could run an instance of the service using the Service Source Code you make available", under the SSPL.
I'm not familiar with this concern for the AGPL itself.