I had to check as I was planning a visit later this year and the shuttle is a key part to our visits here is the response I got from the hotel. By the way it cane super fast 😄👍

"Warm greetings from Hyatt Regency Thessaloniki! Kindly be informed that our hotel offers complimentary shuttle services to and from the city center of Thessaloniki on a daily basis. The shuttle departs from the main hotel entrance and drops off passengers at the White Tower of Thessaloniki. Kindly be advised about the shuttle bus schedule in the attached image. We remain at your disposal for any further assistance you may require. Kind regards,"

So seems like they did not communicate it well on your visit