I’m going to approach it a bit differently. First, I don’t think there are any magic numbers as far as space for chickens go. We keep them in so many different conditions, climates, and circumstances using so many different management techniques with so many different flock make-ups that there cannot be any one magic number that covers us all.
Commercial operations have proven that you can keep chickens in as few as 2 square feet per chicken with no run. They normally trim the beaks so they can’t eat each other and use other management techniques that we normally are not going to do. They also use chickens that have been specially bred to take confinement really well. They are all hens too, no roosters. If you have a set-up where they are never locked in the coop but always have access to more space out of doors, then 2 square feet is actually plenty in the coop. But that’s not just 2 square feet in the coop, its 2 square feet plus a lot more in the run which is always available.
If you leave them locked in the coop during most of their waking hours with no run access, 4 square feet is pretty darn tight.
It’s not a magic number of square feet in the coop that counts. It’s a combination of space, flock make-up, climate, and how you manage them.
There’s also the thing that they may not eat each other if you give them a certain amount of room, but you will probably have to work harder if they have less space. And if you give them the absolute minimum amount of space that requires a certain management technique to make it work, then you have no flexibility in dealing with a problem if one develops.
I recommend you give them as much space as you can stand instead of shoe-horning them into as small a space as you can.
Instead of answering if the roost increases the square footage of a coop (which I think is as nebulous as asking how big is a ball of string), roost space can possibly help the carrying capacity of a coop/run system if you ares hort on roots space. Chickens have developed ways for weaker chickens to live with stronger chickens. The way this works is if there is a confrontation the weaker runs away or the weaker avoids the stronger to start with. This means they have to have room to run away or room to avoid.
If you can give them room to avoid the bullies by adding perches or roosts, yes it can help the carrying capacity of the coop by adding more roost space. But if they already have enough so they can avoid or escape the bullies, adding more won’t help.
It’s not unusual for my younger birds to be up on the roosts in the morning while the older hens are on the coop floor. The younger are using the roosts to avoid the older hens. Since I have enough roost space for them to all get away from the older bullies, adding more roosts will not increase the carrying capacity of my coop.