You guys should also check out Typst https://typst.app/. It is a lot easier than LaTeX even though not as powerful. It has meaningful error messages making the debugging a lot more user friendly.
The Typst compiler is available under the Apache License 2.0.
The web app at https://typst.app is proprietary but also completely optional. You can use Typst with only a text editor supporting the LSP (VSCodium, Kate, Atom, ...), typst-lsp (Apache-2.0 OR MIT) and the Typst compiler.
Well yes, but also no. You can't reproduce a book because that violates copyrights.
Open source in this context just means that nobody owns the book, you can reproduce it however many times you want, and distribute it where you want as long as you include the original license in the reproduction (MIT license).
Also, there's a bit of a colloquial understanding that others are able to contribute or fork the original source material.
But "open source" doesn't even mean that you can reproduce it or use it for free. It just means that you can see the source code. The permissiveness, as you mentioned, lies in the licensing.
So I still think that it's a complete misnomer.
I mean, it's called "LaTeX by example", so there's a pretty good chance it's written in LaTeX, which you do indeed compile to get the PDF or whatever output you want.
Also, just having access to the source doesn't make it open source - that requires more freedoms. For example, here's GitLab Enterprise Edition source code, fully functional and ready to be used. And also officially described as the proprietary edition of GitLab by the GitLab company itself. Why? Because its license pretty much boils down to "you can use this only for testing and development, unless you have paid for it".