Technology connections on YouTube did a video on mini fridges a while back. He focused on the peculiarities of one specific model, but one of the things he did to try addressing some of the issues with uneven cooling was add a fan, and he found that it didn’t really help and made things worse in other ways.

IIRC, the fridge was designed expecting that certain parts would be cooler than others and accounted for that in how the compressor cycled on and off, but with the added airflow those parts stayed warmer than expected so the compressor never shut off.

This fridge very well might be different, and maybe the fan is helping in your case, but you might want to check that video out so you have some things to look out for in case it’s causing other issues that you may not be thinking about.