I think you’d actually need to create a plugin to enqueue a CSS file on all sites.
You can create a plugin with a plugin like this: https://wordpress.org/plugins/pluginception/
Then you can use a function like this inside of it:
add_action( 'wp_enqueue_scripts', function() {
wp_enqueue_style( 'network-style', plugin_dir_url( __FILE__ ) . 'style.css' );
} );
This assumes the style.css
file is in the root of your plugin folder.
Then you can network activate the plugin, and your file should be active across the network.