Turkish Airlines Flight and Airport Procedures Issue During Holiday Travel

I booked a five-person flight ticket months in advance for my family to travel from Istanbul to Diyarbakir on April 6, 2024, at 5:40 AM, with a return on April 13, 2024, at 8:30 AM to celebrate Ramadan. On April 5, 2024, we completed our check-in on the official THY website. We arrived at Istanbul Airport 1 hour and 15 minutes before our flight and queued for baggage check-in. During this time, my eldest son obtained our boarding passes via kiosk to save time. While waiting in line, we noticed that the number of staff at the counters was insufficient, causing delays. When it was our turn, the female staff member informed us that the counter had just closed and they could not accept our baggage, although we could still board the plane. We asked if there was another solution since we couldn't travel without our baggage. The staff directed us to counter 44, stating that we could complete our process there. At this point, we had 42 minutes left before our flight. We moved to counter 44 as instructed and waited for about 15 minutes. When it was our turn, the staff there told us that there was no difference between the counters and that they could not accept our baggage. We asked for assistance and were told to quickly proceed to ticketing to put our tickets on hold, so we could at least recover part of the cost. We rushed to ticketing and did as advised, only to learn that a portion of the total fee would be deducted.
In our beautiful country, where it is often stated that citizens are treated as first-class, I leave this negative experience with THY to everyone's conscience. I believe it is our natural right to expect state-representing institutions to be solution-oriented in such negative situations. For instance, some simple solutions that come to mind while writing this could be: Could we have traveled as planned and sent our baggage on a flight two hours later? Or could it have been suggested that the other four family members board the plane while another flight was planned for us?
After all these difficulties, I request the prompt reimbursement of our financial loss and extend my regards.