Turkish Airlines Refuses My Pet and Denies Full Refund

I purchased a ticket for my Turkish Airlines VSR757 flight with a PNR code and was directed to make a reservation for my pet through the app. The app first made me select a seat, then refused to confirm due to 'full capacity.' Customer service is not helpful at all. They charged me for both the flight and the seat, causing me inconvenience. Additionally, they offer no extra services for pets, treating them like hand luggage by placing them under the seat. When I tried to book a ticket for the next day, they said they couldn't guarantee a pet reservation, meaning I would have to buy another ticket without any clear information. They shamelessly claim the issue is my fault and won't give me a full refund. Is there any logic or fairness in this? I have never had a flight without issues. Either confirm my reservation or give me a full refund. I would never choose them if I weren't forced to.