The 4 square feet in the coop along with 10 square feet in the run is a rule of thumb used by some on ths forum that will keep most people out of trouble in most climates and under most conditions. In Northeast Texas and with a run that size, if you don't leave them locked up in the coop for very long when they are awake, you should be fine with a coop that size for that number of chickens. The amount of space a chicken actually needs varies a lot, depending in the individual chicken, how you manage them, and how many you have. It's the combination of coop, run, and free ranging space with the way you manage them that counts.
I'm a huge advocate of providing as much space as you can. Not because I pamper my chickens but because I find I work less if I provide more space. For example, consider poop management. I firmly believe the less often I have to clean out my coop, the better. Besides, the more room I have to play with, the more flexibility I have in how I manage them.
I will mention a couple of things. Another rule of thumb on this forum is to provide about 1 nest for every 4 hens. You'll find that they will probably use a very few of the nests you provide even if you stick with this 1 for 4 ratio, but I would not provide ten nests. With that number of hens, 5 or 6 nests will be plenty. If you hang those external nests, they can be tedious to build. I provided external access to my nests and never use it. I prefer to go into the coop to look around. I've found possums and snakes in there when I went inside, plus once a hen was dead on the coop floor. I just prefer to go in and look around. If you were building a different type of coop, my suggestion would change but with walk-in coop, I really like walking in.
The other thing I'll mention is that building material normall comes in 4' and 8' dimensions. With the exception of the roof, you could probably build a 8' x 12' coop instead of a 6' x 12' for the cost of an additional sheet of plywood and maybe 2 wall studs, do less cutting of materials, and have less waste. The roof will cost more though. That extra cost of the roof may be relatively substantial to span the extra 2 feet width and provide overhang for drainage. A lot of that depends on where you are getting your building materials and how you build it. There are trade-offs and decisions in everything.