i think AGPL only makes that requirement if you give out YOUR version to users. If you are just using for yourself or internal team, AGPL does not require you to publish those changes.
AGPL doesn't make any distinction between public vs private use. If software you write depends on or extends AGPL code, it must also be licensed as AGPL, period. You do only need to offer the source code to users of the software, but that is still a burden, especially when all you are doing is updating config files.
as far as i understand the license requirements don't get triggered by your own employees because they are bound to you by the employment contract, so it's like sharing with yourself
If I use the software privately, can we just say that I as the only user distributed the modified code to myself automatically?