I Missed Turkish Airlines Flight Due to Baggage Delay and Couldn't Get the Refund

I purchased a ticket from Turkish Airlines for the flight on 19.01.2024 at 07:50 with PNR number VKI7RB for three people. We completed both check-in and online ticketing. After checking in two suitcases, the baggage counter closed while I was about to check in my suitcase. They directed us to the 'Supervisor,' where we had to wait in line again. Despite repeatedly informing them that we would miss our flight, we spent about an hour and a half trying to check in the suitcase. Eventually, they told us they couldn't accept the luggage. We rushed to the gate with the suitcase, but the gate had already closed. We were redirected again for a new ticket or cancellation, but they admitted an operational error and said they couldn't do anything. We later learned from employees that they overbooked the flight and knowingly caused inconvenience. I demand that Turkish Airlines acknowledge their mistake and take appropriate action.