Ah, I found it: The "Compose Multiplatform Plugin...

# compose

[Melchior Grutzmann]

Ah, I found it: The "Compose Multiplatform Plugin" is not sufficient, in addition you need to install the "Kotlin Multiplatform" Plugin. Currently that is not compatible with IntelliJ 2024.1.2, only with Android studio.

Then the second run target shows up.