I am seriously considering using Kotlin on a greenfield Android project, but am concerned about knock-on implications, the most significant of which is a minimum required AP
No. There's no such requirement for the API level as these two are not directly related. Anyway, see official FAQ
Which versions of Android does Kotlin support? All of them! Kotlin is compatible with JDK 6, so apps with Kotlin safely run on older Android versions.
Which versions of Android does Kotlin support?
All of them! Kotlin is compatible with JDK 6, so apps with Kotlin safely run on older Android versions.