Is it possible to debug the Kotlin code of my web app from IntelliJ, by using breakpoints? Or if another way is recommended, please tell me where to start. (Maybe this is a question for #compose-web because it's a compose for web project?)

Given that your source maps work (you're seeing Kotlin code in the browser's dev tools), have you checked this? https://www.jetbrains.com/help/idea/interactive-debugger-console.html