I'm not in it for the rightness and wrongness and virtue and exercises of justice to the carrots, I'm in it for your request as to whether peeling a carrot counts as processing, which it does, as sometimes the most banal of examples illustrate a tapestry of lived complexity.
A “sandwich” doesn’t have an explicit general meaning, but almost nobody would classify a pizza as an open face sandwich.
Likewise, the vast majority of people would consider a carrot (peeled or otherwise) “unprocessed food” and would consider cheetos “processed food”.