I Missed My Turkish Airlines Flight Due to Incorrect Guidance from Check-in Staff

On 21-09-2023 at 14:10, I had a THY flight from Istanbul to Amsterdam, but I missed the flight due to incorrect guidance from the THY staff at the check-in/visa process. Here are the details:
1. I did online check-in a day before.
2. At 12:45, I saw from the check-in board at Istanbul airport that the check-in for flight TK1953 Istanbul-Amsterdam was open at blocks E and F. Since I had one piece of luggage, I went directly to block F.
3. Seeing a long queue at F, I approached the staff at F23 with my child to ask for a fast pass. Our conversation: Me: Hello, I know there's a special pass for families, is there a fast pass? F23 (Male with glasses): There is no family pass here, it's at passport control. Me: We have little time left, can you help us? F24 (Female staff): Which flight and what time? Me: Amsterdam flight at 14:10. F24: You still have plenty of time, wait in line.
4. Following the staff's guidance, I waited in line for about 40-45 minutes. When it was my turn, the check-in staff gave me a late boarding card and said we were late. When I mentioned the guidance from the staff at F23 and F24, they said they couldn't help.
5. I went back to the staff at F23 and F24, explaining that I missed the flight due to their guidance. They first claimed not to remember me and then said they didn't hear me. When I asked how they responded without hearing, they directed me to the THY ticket office at Istanbul airport, saying they handle visa processes and the ticket office staff would assist me. They refused to give their names or employee numbers.
6. The staff at the THY ticket office said that since I did online check-in, I could still board the flight and directed me to the F44 supervisor.
7. I explained everything to the supervisor. He said the only thing I could do was file a complaint, and if I was right, THY would issue a statement to my company and cover all my losses based on camera and audio recordings. However, despite filing two complaints on the THY website, I haven't received a response after two weeks. Complaint numbers: #TK-94463** and #TK-94753**.