Does Kotlin DSL supports everything that groovy supports, so I can ditch groovy scripts altogether?

it should, but good luck finding the equivalences

also having similar problem, there is guide to convert groovy gradle to kotlin gradle, but it is still an effort as most article around are groovy-based

equivalences for what? plugins?

yeah, documentation atm is terrible

if I have a plugin written in groovy for groovy based gradle script, can I still use it in kotlin based scripts?

Yes, the only thing you should be careful in your groovy plugin is not to expose Groovy Closure and use Gradle Action instead ( so it's language agnostic )