how to know that a wordpress plugin support using API?

There’s no trick. If a plugin has an API that is intended for you to use externally, such as in a React Native app, then its developer would document it.

So all you can do is check if the plugin has developer documentation, and whether that documentation includes a REST API or similar. For example, WooCommerce has a REST API for some of its functionality, which is documented here. If a developer has created something like that for their plugin, then it’s probably safe to use their API in your app. If they have not, then it either doesn’t exist, or is not safe to use.

While some WordPress functionality, like Custom Post Types, can result in certain plugin data being accessible via the WordPress REST API, you can’t be sure of what data and functionality is accessible, in what format, and whether it’s safe for external use, unless it’s documented.