This is what a friend experienced a couple of month ago. He had to cancel a separate booked flight, because his luggage misconnected. As there were no interline agreement, the airline refused to send it to his final destination and made the valid point, that is not within their responsibility, that he had a separate ticket to another place. You might be lucky to get the luggage in the region around the airport but this would not cover Croatia or Italy.

Of course it is ymmv ...