This article, and the related video, do a good job of explaining the overall architecture
https://blog.jetbrains.com/kotlin/2021/10/the-road-to-the-k2-compiler/
I'm definitely not a compiler engineer, but I don't think Kotlin is a "standard transpiler" in the sense that the JS world would know, for example. Kotlin is a proper compiler with a common "front end" that parses the source code into an Intermediate Representation (IR), and then passes that IR to one of the "back end" targets for binary code generation. A transpiler is more source->source processing, while Kotlin is source->IR->binary (which in JS happens to be "readable source code", but it's still the JS "binary" as far as the compiler is concerned)