Wondering if anyone might have some ideas on how to fix this...

Fridge wasn't cooling properly and noticed there was no airflow. Ordered a new fan and when I was getting to the old fan and restarted the fridge I noticed the old fan worked for a bit and then turned off. I went ahead and replaced it however the new fan seems to be shutting off before the fridge actually cools down properly. The coils are definitely cold with ice all over them.

Is there some type of thermometer broken somewhere that the fridge thinks it is colder than it actually is or has anyone had issues like this before? Or do fridge fans just cycle off and on and I need to be patient and see if it cools down. Also it will turn off even when condenser is running to catch up.