Looks like the dependency in the image you shared, react-native-responsive-view-port, hasn't had a new version in five years (https://www.npmjs.com/package/react-native-responsive-view-port). I'd suggest seeing if you are able to comment out or remove any code that relies on that package, and then remove it for now, and repeat for any other small dependencies without recent versions.
You may find it's only a couple of small dependencies that you need to do that for in order to get the app building at least, and then you can review whether you can either a) switch to a different package that provides the same functionality but has been updated more recently to work with current React Native or b) fork the old dependencies to bring them up to date with the React Native version you are using (which may or may not be a lot of work depending on the functionality of the dependencies).
This may be useful in general for migrating your project to a more recent version of React Native: https://reactnative.dev/docs/upgrading.