Is it wise to run an API server with Kotlin/Native or is it preferred to run it with the JVM for now?

Heavily depends on the situation. Kotlin JVM is the better choice to use with REST servers, web services providing web APIs, and general server projects. With Serverless and server projects, where a resource constrained device (aka anything SBC based like a Raspberry Pi for example) is the server Kotlin Native is a much better choice. If you are unsure then it is best to stick with Kotlin JVM.

Jvm