Unfortunately the interoperability of Kotlin with Javascript is not seamless like with Java. It seems like the Vue kotlin project hasn't been updated for 4 years.
Getting Kotlin to work with an entire framework is probably a non-trivial undertaking. Could be very educational, but unlikely to be trivial.
I think the official JS wrappers are probably you're best starting point, but right now, the supported framework is React: https://github.com/JetBrains/kotlin-wrappers