Beef stew was left cooling on the stove for like six hours
Seven hours is not much, starting with a sterilised stew. Use you senses. Are there bubbles? Does it smell strange? Have a mouthfull, does taste off? If not, I would eat it. In fact, I wouldnt even give it a second thought after seven hours starting from fresh.. but US regulations, yes, would say it cannot be served. Good you are not running a restaurant, but this is just home cooking, er?..