Turkish Airlines Didn't My Ticket Refund

I couldn't get a refund. I purchased tickets with Turkish Airlines for a trip from Izmir to Istanbul and then from Istanbul to Abu Dhabi with two passengers and two dogs. Before buying the tickets, I checked the pet availability for my desired flights with customer service and learned that there would be a discount through the app. I started making the necessary reservations through the app. I added my first dog to my flight without any issues. When I tried to add my second dog, I encountered a problem. Before reaching the payment section, I called Turkish Airlines customer service and explained the issue I was having while adding my second dog. The representative told me that I could add the dog through the extra services section after purchasing the tickets. I completed the payment but couldn't add the dogs for either flight through the extra services section. I called customer service again and explained the situation. I learned that there was no longer availability on the flight that had availability just a minute ago. Since I had to fly with my dogs, I requested a refund, but it was not accepted. They advised me to create feedback for the complaint. The Turkish Airlines representative stated that the previous representative had given incorrect information and that if I couldn't add the dogs at that moment through the app, I wouldn't be able to add them later either. I created a feedback form for the complaint and refund and sent all the information multiple times. They said they would review the call records and the dates of the conversations and get back to me. In their response, they confirmed that they had informed me I could add pets after purchasing the tickets and that they would make the necessary warnings. I did not receive an answer regarding the refund and created feedback again. I called multiple times, and this time they said they couldn't refund because I had searched for the Izmir-Istanbul flight. I created feedback again and received general information. It was not specified that I needed to buy a special ticket for this flight and then add the pets through the extra services. I trusted the information I received from the customer service representative, bought all my tickets, and completed my payment, thinking I could add the dogs through the extra services. If they accept that incorrect information was given, they must take responsibility for the subsequent issues. They need to resolve the problem caused by them and refund the tickets.