> but what about using some other library that installs React as some dependency?
I think that still counts as "using react".
> Does using JSX also count as using "React"?
I think that if you use a custom JSX compiler instead of the one that comes with React then you could be clean. JSX itself is just a programming language and cannot be copyrighted.
> I just feel that what exactly constitutes using React is very vague esp
I don't think that is vague, actually. In the end, what matters is if the whole system includes React source code in some way or another.
> and associated technologies, eg the idea of Virtual DOM
Associated technologies are not covered by copyright. They could possibly be covered by patents but that would be a whole different can of worms.