You’re talking about a couple of different things. Roosts are what they sleep on at night. Perches are places chickens like to hop on during the day. They just often like to be up high.
I’ve tried tree limbs, 2x4’s flat side up, and 2x4’s with narrow side up. I’ve determined that people care about what you use much more than my chickens do. And the chicken’s feet do disappear under feathers when they squat down and fluff up their feathers to protect against cold no matter which they are on.
The narrow side of a 2x4 is 1-1/2” by the way, not far off your 1-3/8” rods. As Egghead sort of said, the problem with those curtain rods may be that they bend too much more than that the chickens can’t hold on. You’d be surprised how well they can hold onto wood. A 2x4 on edge will be a lot stiffer and won’t bend as much. But that depends on how many chickens you are supporting and the span.
As others have said, chickens normally like to sleep on the highest spot they can get to. That doesn’t have to be a pole, it can be a nook or cranny or even a flat piece of plywood. But poop doesn’t build up that much on poles so poles (or beams) are normally used. Chickens poop a lot when on the roosts. You don’t want them pooping in your nests. So you want the roosts higher than anything you don’t want them pooping in.
The way I determine how high to put the roosts is first determine the height of my floor, including bedding. Then situate the nests. Some people have nests right on the floor, some hang them high enough they don’t have to bend over to get the eggs. Then install the roosts noticeably higher than the nests. What’s noticeably higher? If the roosts are right at the nests 6” might be enough. At the far end of a large walk-in coop one foot will probably work.
There are some other considerations. Ventilation is very important in a coop, even in really cold weather. You want to be able to exchange good air for bad. In warm weather it doesn’t matter, the more ventilation the better, but in truly cold weather you need to get air moving without a cold breeze hitting them on the roosts. I’m not talking about a gentle draft like you get around a window in your house that doesn’t seal really well. I’m talking about a breeze that causes wind chill and ruffles their feathers. There are different ways to achieve this but my favorite is to have openings over their heads when they are on the roosts. That way any breezes are safely above them yet you get good air exchange.
I don’t know if this applies to you or not but I often integrate chickens. When you integrate the weaker chickens need a safe place to get away from the stronger. This is often my roosts when they are all in the coop. I often find the young ones on the roosts away from the adult on the floor when I open the coop in the morning. So I want my roosts high enough that the adults cannot peck the toes of the chickens on the roosts. That gives them a safe haven.
Then there is the problem with the mount and dismount. Chickens spread their wings and fly up to the roosts. They need enough clear room to fly up. If things are really tight with a lot of clutter in there, you probably need steps that they can hop up instead of spread their wings and fly. Mine normally prefer to fly down when they dismount. I’ve seen mine on several occasions launch off a 4’ high roost, fly forward about 7’ make a 90 degree turn, fly through my door, and land in the run. These are mature full-sized fowl. They are not extremely graceful fliers but they can fly. But the higher the roosts the more clear space they need to land without banging into walls, nests, feeders, waterers, or other things. So make the roosts high enough that they want to sleep there but don’t go overboard on making them really high.
As an aside, in my opinion if they have enough room to fly down, they are a lot less likely to hurt their legs when they get off the roosts. But that’s just my opinion.
As Oldhen said, don’t be shy about providing enough roost space. It’s normally not a problem when they are all the same age and have worked out the pecking order, but sometimes a chicken (practically always a hen) can be a brute on the roosts. Where they sleep is determined by pecking order and they can be pretty brutal enforcing those pecking order rights. I especially notice his when I’m integrating. Sometimes it’s so bad the younger chicks leave the roosts and find a safer place to sleep. That was usually my nests until I put up a separate roost lower than the main roosts and horizontally separated. It’s not so much roost space for chickens, it’s giving enough room they can get some separation. It’s probably not a huge concern for but maybe more of a fix if you start to get chickens sleeping in your nests.
All that above is about the roosts. As far as perches, have fun with it. Try different things. They do like to perch. I’ve seen chickens try to perch on a 3/8” piece of plywood I was using as a guillotine type door on a separate coop. Young chicks didn’t have much trouble with it but full sized adults would fall off in less than a minute, then fly back up and try again. Sometimes chicken TV is better than anything on cable or satellite. You can hang swings or put something in there for them to hop up on. One issue with this is that they might prefer to sleep in the run instead of in the coop if you give them perches out there. If you don’t consider your run predator proof or if you have a really brutal winter this might be a concern.
If your run does not have a top on it, they might use a perch as a launching pad to hop over the fence. Maybe something to consider.
I know I make it sound complicated. It’s not really that bad. Just make them high enough and out of breezes in winter if you have cold weather. And welcome to the adventure. It’s a fun journey.