I am not sure if the KMP plugin in Intellij/AndroidStudio already support more than Android and iOS.
I pull the project and use the sample templates, at the end is all you need. What Android Studio does is generating those build.gradle files for you.
These are the stable examples:
https://github.com/JetBrains/compose-jb/tree/master/examples
and these are the unstable examples:
https://github.com/JetBrains/compose-jb/tree/master/experimental/examples
There are major differences between the two types of projects, the stable and the experimental ones.
Decide on what to use stable/experimental and pick one sample that has web.
The experimental are supposed to be the future