I've spent a few hours figuring this out. Reloading after reloading. I've had this happen with my 3rd and 4th kitchen I built.
The problem for me was the trays (although I see plates on your screenshot, but maybe someone else had my problem). For some reason (has to be a bug) new trays don't come with any of the kitchen equipment after you already have like a kitchen or 2 running. The thing that solved it was connect another kitchen to the new kitchen, and it has to be in that order. One of the shifts later some cook will bring plates to that kitchen from the other kitchen and then they start eating.
Also I notice that the plates are unevenly distributed among all my kitchens, one has literally piles and piles of dirty and clean trays, while another (which about as many cooked meals) has only a few piles of clean ones. For a test I've connected every kitchen to every other both ways and the distribution stays the same.
Anyways the initial problem really should be fixed because the default food distribution won't get any trays in and your prisoners will eventually starve with serving tables full of food in front of them.
Btw @OP, your minimal security prisoners have more free time than an average free working man lol
