Youtrack was made long before Kotlin so I suspect the rewrite just wasn't worth it
TIL - YouTrack was first released in 2009, Kotlin in 2011, so I wouldn't call it long before, but definitely before. Guess I'm more interested in programming languages than in task management tools, that's probably why I have been aware of Kotlin longer than of YouTrack...
Thing is, iirc Kotlin is mostly compatiable / interchangeable with Java so they could write any new code in Kotlin.