What are the costs of pursuing this dive?

Thanks to the internet, and a plethora of free online resources, you can pursue this dive for free, even from your local library, as long as you can secure an internet connection and have access to a computer that you can code on. Yes, you can even code from a library, because you can use what's known as an IDE (integrated development environment)---more on that later.
The web is littered with free react tutorials. There are hundreds of good quality Youtube videos that can teach you the basics and thousands of articles if you prefer written content. 
You can be a competent React Developer without having to spend a dime (save for bandwidth costs). There are also dozens of free books that can take you from beginner to intermediate that are absolutely free. 
If however, you want to learn the advanced stuff, you may have to spend up to a few thousand dollars depending on which route you choose. 

Bottom line, you can get started with some really affordable Udemy courses or decide to attend some really expensive in-person boot camps. The choice is yours. You can even get started for free, and that’s probably the best route to take initially.