So without further ado, here are your questions, and my best responses...
ANSWER: Good line cooks take a lot of pride in working clean and having an organized station — your cleanliness shows everyone in the kitchen that you know what you're doing. The same goes for chefs; their kitchen reflects their leadership. That's how it works.
All that being said, mess and dirt are occupational hazards in the professional kitchen; sauces spill, hot pans get dropped, and cooks with dirty clogs shuffle around the kitchen for 10+ hours daily. So yes, kitchens get dirty, but whether or not they remain that way at the end of the night is a reflection of the chefs working there. If you are nervous about food safety when dining out, check the state of the restaurant's dining room and bathroom when you arrive.
If the managers care about the cleanliness of the kitchen, the dining room is definitely spick-and-span. Also, I advise getting to know the people cooking at your favorite places. Make an effort to thank the chef if you see them walking through the dining room and introduce yourself! Look out for how the chef interacts with their employees and other guests.
I've worked in kitchens that deck-washed* the floors every night and places that mopped mayyyyybe once a week. You can guess which one was led by a respectful chef who cared deeply about their restaurant and which was run by a chef who didn't. Moreover, word-of-mouth is still the best way to find solid restaurants with good people w.