I'm not a believer in "Magic Numbers" for chickens. We keep them in so many different climates, under so many different conditions, and use so many different management techniques that different numbers work for different ones of us. The numbers you mentioned will keep most of us out of trouble most of the time. They are more than the absolute minimum many of us need. But they are not at all over the top for many of us. I understand if you don't have experience with chickens, you need some place to start. Four square feet in the coop with ten in the run per chicken is a good place.
A few things I'll mention. Building material often comes in 4' and 8' dimensions. If you plan your coop with that in mind, you can often build a larger coop for the same amount of money and with less cutting and material waste. That applies to your run too. I don't know how you plan to build it, but look at the length of a roll of wire so you don't have as much waste. You can often make the run a lot bigger for very little extra money. That can really depend on how you buiild it though.
I prefer making the coop and run longer and narrower rather than square if you are going to cover it. The wider your coop and run, the longer distance that lumber has to span. You can wind up with pretty heavy lumber in long expensive lengths if you don't consider this. In your coop this is probably not an issue, but if you are going to cover your run, you might think about it. Depending on where you live, you could have snow and ice loads. About anywhere, you can get some strong wind loads. Don't build your roof too weak.
I find that the more space I give them the less hard I have to work. My coop is oversized for my flock. I don't put in much effort in poop management, for example.
With extra space, I have more flexibility in dealing with problems. If I need to leave my flock locked in the coop for days at a time, I can. If you plan on integrating new chickens or having a broody raise chicks with the flock, extra space comes in really handy.
Instead of trying to figure out the minuimum space required for a certain number of chickens, maybe think of your number of chickens and then think how you can provide plenty of space for them.