Lug Nuts Liability w/ dealership

I had a tire rotation done at 5k miles in July 2025 on my 25 Turbo Premium and 3000 miles later in November i found that one of my lug nuts was recently missing (I check the car routinely, all of my lugs were present two days prior). These are the custom lug nuts with wheel locks that are available as an accessory purchase at mazda. I replaced it with a 19mm lug nut that I had to purchase (dealership never gave me the stock set of lug nuts I realized that only in that moment). I decided to retorque the entire wheel to 80 ft-lb spec just to make sure that everything was secure and to my surprise all of the nuts were loose. Two of the other three wheels had the same situation.

Is the dealership liable for covering the cost of the missing lug nut or am I expected to eat this cost? Also can I contest the rotation fees since they clearly did not torque my wheels back on adequately?