Here's a fix: Place a serving table in your staffroom and make sure to have places to sit and they will eat the staff food and the cooks will clean the food trays

If you have a serving table and places to sit in your staffroom the staff will eat and the trays will get cleaned

When I have a canteen for the staff, then i have to make it "staff only" but then when the guards eat, they leave their food trays on the tables and then the cooks will not clean them, or even pick them up and stack them. The job is queued, "Todo: Store in Canteen" (to stack then...