They are going to love that set-up. It’s really diverse.
I don’t know your climate, where your coop will be situated, anything like that. During the times of the year when your get enough rain and it’s warm enough, your grass will be great for them. In winter or if it gets so dry your grass stops growing or dies, they can do more damage to it. Unless you are in an area with really dry summers, you should be OK. The carrying capacity of your land depends a lot your climate and time of year.
They will spend some time in the bog area but I’d expect most of their time will be in the wooded area. They like the shade plus they like being under cover. Scratching in the leaves is so much fun plus they find all kinds of good things to eat. But they will be all over.
I have an area I call the bog. It’s not a permanent wet area with a seep, a wet weather spring and low area that often stays wet, but it does dry out enough in the heat of summer that I can mow it. Mine would visit it daily, they really loved the frogs, but they did not spend that much time there. It is usually tall grass, no trees for shelter or cover from hawks.
What I’d expect with 40 chickens on an acre is that the area near the coop or where you feed and water (with the bog and seep you may not need to water most of the year) is that the area where they most hang out will show signs of wear. They will dig holes to dust bathe in. They will scratch a lot. It’s possible their poop will build up to a level that most things can’t grow, just too much fertilizer. I think you’ll be OK with 40 chickens on that acre unless you live in some extreme climate area. There will be some bare areas but not that much.
I’d position the coop away from the bog/seep. Your coop needs to stay dry anyway. A wet coop can be dangerous from a disease perspective plus they stink when wet. With the coop away from that bog/seep area I don’t think you’ll see much if any real damage down there.