I wasn't surprised that it's written in a JVM language, but I was surprised that that language is Java, not JetBrains' very own Kotlin...
You can port files from Java to Kotlin by pressing a button, but Jetbrains has generally not done bulk ports. They leave it up to individual devs to convert a file when it's being worked on, if the diff and VCS history pollution is worth it.
Youtrack was made long before Kotlin so I suspect the rewrite just wasn't worth it