It seems Android Studio build's log doesn't show the specific errors. By checking the xcode I can see a build issue:

Which the issue is with room's config for IOS. By adding the following line in framework block inside cocoapods block, the build is successfull:

kotlin {
    cocoapods {
        summary = "Some description for the Shared Module"
        homepage = "Link to the Shared Module homepage"
        version = "1.0"
        ios.deploymentTarget = "16.2"
        podfile = project.file("../iosApp/Podfile")
        framework {
            baseName = "ComposeApp"
            isStatic = false
            transitiveExport = false // This is default.
            linkerOpts.add("-lsqlite3") // I had to add this line
        }
    }
}