Yep, AGPL can run alongside proprietary services without issues, and if you host it without modifications, you don’t have to share anything. But if you modify it and make it available over a network, you have to provide the source to users.
Mathesar, however, is GPL, so you only need to share modifications if you actually distribute the software itself.
When I was at a big tech, the interpretation by their lawyers was that by running AGPL, we will have to open source everything in the network to users. The problem is in the definition of "Modification" - Per [AGPL](https://www.gnu.org/licenses/agpl-3.0.en.html#:~:text=To%20%...):
> "The "Corresponding Source" for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities."
This can be interpreted as even modifying any configuration to allow the software to run on your own infrastructure. Obviously this is a very aggressive interpretation but the lawyers didn't want us to test this phrase in court so all AGPL software had a blanket ban.
Mathesar, however, is GPL, so you only need to share modifications if you actually distribute the software itself.