or you can use the application plugin, and pass args by configuring the

run

command

Prefer to keep the run task unchanged to cover th use case of running a program without args.

Just create custom run task, it's standard way to do that with shadowJar and application plugin. Actually, shadow plugin already provides task runShadow, that builds executable shadow jar and run it, if you don't want to change it and add custom arguments, just create a new task of the same type with custom args

There doesn't seem to be a way to create a custom run task with Kotlin DSL.

What do you mean? Of course you can create custom task in Kotlin DSL that based on some task type. Your problem with creating of JavaExec task related to some other problem, not to Kotlin-DSL, I’m pretty sure