Just to understand: When running "./gradlew -t run" changes to the Kotlin code result in an automatic reload of the browser. Changes to *.html files (in resources) do not reload the browser. Correct?

I think the changes are immediately available, but they do not cause the autorefresh. So if you manually refresh your page after say index.html changes (without restarting build/devServer) they should be present

Yes - the changes are present when reloading.