And you are obliged to share the changes you made to the source code publicly. You can share the way you choose, but you have to do it.
The copyleft licenses don't require to share the source code publicly, they only require to give source code forward to downstream users, who may or may not contribute back upstream to the original project. In the AGPL case, that would be only users that you let have network access to the modified AGPL software.
Well, you're running the upstream software in that case, so you don't have to share anything, which is logical.
> The copyleft licenses don't require to share the source code publicly, they only require to give source code forward to downstream users...
Well, if you're distributing the software to downstream users via network, you need to share the source code via network. It's also logical and straightforward.
You can't tell that it's GPLv3 and binaries are here, but I won't give you the source. You have to.
If we were in 80s, I'd happily mail you a check and envelope to mail my floppies. One optional set for binaries, and one set for the source.
In both cases the practicality is the same.
Otherwise you’d be fine not distributing it at all (besides some occasional internet outrage).