It's not quite clear what targets you're wanting to support. React Native sounds like you want ios and Android but mentioning wasm sounds more like android and web. You can use kmp/kmm to share code with iOS. Most people still do the iOS interface using swift though. Doing UIKit in code isn't a great experience and trying to wire up storyboards to Kotlin view controllers requires some hacks. You'll still see a good amount of code sharing if you go down this route.
If you're looking to share code between android and web, your shared module could include a JS target, no wasm needed. There is Compose for web. From what I've seen it is geared more towards generating html than ui components. You won't easily lift your Android compose code and just run it in a browser. It's a similar situation with React and React Native. Although React Native Web muddies the waters because it's supposed to let you take React Native code and run it on the web.