To import your Godot project into react-native, you need to generate a pck file that basically packs up all your game assets, scripts etc. It's a convenient way to pack your game into a single file.
First, you need to add a export_presets.cfg in the directory of your Godot project. We provide a working example of this file at the root of this repository.
After that, you're now able to generate a pck file, just run ./gen-pck PROJECT_FOLDER_PATH. Be sure you have /Applications/Godot.app set on your machine, if you're using another path or another OS than macOS, just modify this very simple shell at your convenience.
Godot with all features enabled is around 140MB for iOS (arm64). godot-cpp bindings is around 60MB, which is used to communicate with the Godot engine from React Native. So for now, it's around 200MB for iOS (arm64), we might be able to reduce this size in the future.
For example by disabling features that are not needed, removing MoltenVK for iOS in Godot 4.4 (which is around 9MB), not depending on godot-cpp by forking the engine completely, etc. Also, your pck file must be considered in the size of your app. Which can be quite large too if you have a lot of big assets like 3D models, textures, etc.