I don't think anybody is arguing that. However, most people entering this thread understand fast food to mean something like this:
https://www.dictionary.com/browse/fast-food
The "prepared in quantity by a standardized method" is key, and is generally only the domain of larger chains. Ignoring that, colloquially, people associate "fast food" with large, national (or international) chains (McDonalds, Burger King, Taco Bell, etc.) and would not be considering an option like you provided. Fried mushrooms are a niche side in any restaurant segment, but if I had to associate them with one I'd probably say, typically, it would be "fast casual." Food served in this sector is generally made to order without table service (Chipotle, Panera, etc.). Maybe even casual dining, where you have chains like Fridays, Chilis, Applebees, etc.
So what, exactly, are you asking us!