Sorry, I recently activated a "Coming soon..." plugin.
I got my orignal setup working finally, after changing my child CSS.
I deleted "@import..." (parent CSS) and instead created a functions.php in my child theme with this code:
<?php
add_action( 'wp_enqueue_scripts', 'enqueue_child_theme_styles', PHP_INT_MAX);
function enqueue_child_theme_styles() {
wp_enqueue_style( 'parent-style', get_template_directory_uri().'/style.css' );
wp_enqueue_style( 'child-style', get_stylesheet_uri(), array('parent-style') );
}
That did the trick.