ShareLaTex VS latexcgi

you can already self host it https://github.com/overleaf/overleaf

Mostly open source... Here's the repo: https://github.com/overleaf/overleaf. But you can see what features are only available in the paid versions here

Overleaf's license. I highly suggest reading point 10. I only skimmed it, but there are probably other pertinent details.

Look at the project license: https://github.com/overleaf/overleaf/blob/main/LICENSE

the linked repo is archived and it states, it has been merged into overleaf/overleaf

The Overleaf Community Edition is a lite version of our LaTeX editing platform which can be freely self-installed (see https://github.com/overleaf/overleaf for details); and Server Pro is our full, officially supported, paid service. Server Pro is an excellent option for organizations that are looking for the ease and functionality of the Overleaf platform, but require a solution that sits behind a firewall.

> any popular opensource library using AGPL since?

Not quite a library, but overleaf (the online LaTeX editor) is pretty big in the scientific community and it's agpl.

https://github.com/overleaf/overleaf

I think the images are static, so presumably pre-rendered server-side. The editing & rendering on the individual example pages seems to making an API call to a server, which I think is running this [1].

[1] https://github.com/davidcarlisle/latexcgi

You might want to take a look at David's latexcgi. Sources are on GitHub.