Turkish Airlines Flight Delay and Poor Customer Service - Request for Compensation

The Turkish Airlines flight from Istanbul to Washington on August 3 was a complete disappointment. Despite purchasing my ticket 2 months in advance, my 4-year-old daughter and I were placed on standby at the last minute. The flight was overbooked, and those who did not check in online were put on standby. I attempted to check in online the day before, but the Turkish Airlines website gave an error, preventing me from doing so. When I explained this to the staff, they just stared blankly and said, "Sorry, if there are empty seats, we will let you on." Essentially, they made the customer pay for their incompetence.
Our baggage allowance was reduced to 1 piece without any prior notice, and we found this out only at the airport. I expected to take my extra bag for free due to this inconvenience, but they insisted that I would have to pay. They told me, "We don't take the money here; the system is locked; go to ticket sales." I pleaded with them not to make this more difficult, as we were already victims of their mistakes.
After running around with my 4-year-old daughter, we finally found a ticket sales counter, where they charged us $265 for one piece of luggage, while United Airlines only charged $40. This felt like a complete money trap!
The ordeal continued at passport control, where we faced long lines for security checks. Due to the insufficient number of female staff, women passengers had to wait for an hour to be searched. As standby passengers, we were the last to board the plane. Some standby passengers with children were seated separately because there were no available seats for them. These passengers had all purchased their tickets in advance but still faced this inconvenience.
The troubles did not end on the plane either. We waited for 2 hours in an airless cabin, as the flight was already delayed by 2 hours. During the meal service, they informed us that there were no meatballs left and only served pasta. There were no other options available. Most of the cabin crew seemed indifferent and tense.
The final blow came when we waited an hour for our luggage in the U.S., only to be told that our bags had never been loaded onto the plane. At least 20 people did not receive their luggage. I cannot understand why they didn't inform us of this earlier, leaving us waiting at the airport.
In summary, we were humiliated despite paying for our tickets. This experience does not reflect well on Turkey's most prestigious airline.