Turkish Airlines Flight Ticket Refund Issue

I purchased a ticket for the 15:25 flight on 31.08.2023 from Edremit to Istanbul with THY and completed the check-in process in advance. However, due to my illness, I arrived at the airport late. The plane was still on the runway and loading, but we were not allowed to board. We requested a change for the next day, and initially, they asked for an additional ₺2,950 for two people. We accepted and paid with a credit card, but during the process, they said we needed to pay another ₺2,350 per person. When we refused and asked for a refund, they denied it and declared our tickets as forfeited. This is unacceptable from THY, and we demand a refund for our tickets. The plane took off approximately 20 minutes after our conversation. Given that this is a small airport and we had already checked in, we should have been able to board the plane. Instead of facilitating our boarding, they tried to sell us new tickets. I urgently request attention to this matter.