Normally, I'd suggest that you do some building with React before going into React Native, but since you already come from the mobile world, it may be easier for you to pick up React Native almost immediately - that way you'll encounter concepts you're familiar with immediately instead of having to learn Web Development just so you can practice.
Since you're already familiar with programming, rush through a JS course to learn the syntax (particularly the stuff introduced in ES6), keep a tab open to look up the parts you forget and then dive straight into React Native. The only thing I would recommend is that you keep your React Native configurations as out-of-the-box as possible while you're learning so you don't go down a weird rabbit hole trying to configure Webpack etc.
Expect to spend a little time bouncing around between the React and React Native docs as you get a grasp of the concepts, though. React can be a weird way of thinking if you're not used to it - I've found the writings of Dave Ceddia to be really helpful with React.
Thank you for your fast and informative response!
We're a place where coders share, stay up-to-date and grow their careers.
We strive for transparency and don't collect excess data.