The code below will make "Order notes" as a mandatory field for "Local Pickup" chosen shipping method only and will display an error notice if customer try to submit his order for this requirements:
// Validate mandatory "Order notes" field for "Local Pickup" shipping methods
add_action( 'woocommerce_checkout_process', 'local_pickup_order_comment_validation', 20 );
function local_pickup_order_comment_validation() {
// Convert the array to a comma separated string of values
$chosen_shipping_methods = implode( ',', WC()->session->get('chosen_shipping_methods') );
// Targeting any "local_pickup" shipping method
if ( false !== strpos( $chosen_shipping_methods, 'local_pickup' ) && empty($_POST['order_comments']) ){
wc_add_notice( __( "You need to fill up \"Order notes\" with some details.", "woocommerce" ), 'error' );
}
}
Code goes in functions.php file of your active child theme (or active theme). Tested and works.
Related: Make Checkout Order notes field required for shipping method ID in WooCommerce