Thank you for the logs Webtechnz,
Unfortunately, as you mention yourself, they don’t clear up the picture at all! This could be an additional security feature of your server, perhaps the database access isn’t granted on certain kinds of calls. If you wish to try a quick fix, to confirm that these are indeed the clear cache calls, you can add the following code in the functions.php of your (child) theme, to see if this stops the 405 errors:
if( class_exists( 'A_W_F' ) && ! empty( A_W_F::$admin ) ) {
remove_action( 'woocommerce_update_product', array( A_W_F::$admin, 'on_product_update' ) );
remove_action( 'before_delete_post', array( A_W_F::$admin, 'on_product_deletion') );
remove_action( 'wp_trash_post', array( A_W_F::$admin, 'on_product_trashing') );
remove_action( 'untrashed_post', array( A_W_F::$admin, 'on_product_untrashing') );
}