why did our fridge stop working?
Ice build up on the coils limits heat that can be removed, causing the pump to run longer, in addition to the colder temperature requirement. That much is known. This is speculation: The pump running longer possibly caused the motor to overheat.

Electric motors of this size usually have thermal overload protection, they simply shut themselves off if they get too hot.

It's best to adjust temperature in small increments, verifying with a thermometer, and waiting overnight to allow the new setting to stabilize before making another adjustment.