I didn't see the actual size of the storage area versus how much actual coop area is available for chickens. Still you have a lot of room to work with.
Some of the things I like is that the nests are against an interior wall. In Texas that will keep the nests from becoming ovens if they happen to be on a sunny wall. That's a lot of roosts and will take up a lot room as far as you working in there, but you can deal with that. By being spread out like that integration could be a lot easier. You might consider making one 6" to a foot lower than the other to encourage the bigs to sleep on the high one and free up the lower one for juveniles.
I don't see the benefit of the PVC feeders for grit and oyster shell. You are not worried about them getting wet and you very seldom need to refill them anyway. I'd consider hanging a feeder on the run wire (maybe a rabbit feeder) and carrying refills to them one a week, once a month, once a year as necessary. To me it makes the build simpler and it's really not an inconvenience as seldom as you need to refill. My philosophy is that a design is finished when you can't take anything else away, that keeps it simpler with less that can go wrong. Others feel that a design is not complete until you can't think of anything else to add. A lot of personal preference. How are you keeping the feed dry since your feeders are in the run?
I like having the brooder in the coop. I believe it helps integration tremendously if the chicks are raised with the flock. My real preference would be to have the brooder on the run wall so I could fence off portion of the run so I could isolate that for chicks or a chicken in isolation but I can't come up with a workable layout and incorporate your PVC feeders. That's not necessary anyway, I did not have that in my coop and it worked well. I did have a Grow-Out coop on the far end of the run which helped.
There are different ways to do that. The equivalent in my coop would be to put the brooder under a roost and use the top of the brooder as a droppings board. I did the same thing with my nests but that was an afterthought when I needed a juvenile roost to help with integration.
I think it will work fine to make the side of your current brooder next to the coop a wire door that opens into the coop so the adults can see the chicks. You can put another door in the storage area for access to feed and water. I could see some advantages in that for you as opposed to how I did it. If you elevate the brooder enough to slide plastic bins from
Walmart under it and make the floor wire that makes cleaning and keeping the brooder dry about as easy as it gets. When using it as a brooder put something solid on the floor, I've used plywood. Cleaning just means tipping it, I hardly ever needed to scrape. When it is not used as a brooder it is available as a broody buster or an isolation area. My brooder being elevated never interfered with integration but my procedure is likely different than some others. My integration procedure is that at 5 weeks of age I open the brooder door and walk away. When they are all out of the brooder I close the door and leave it closed.
The way I read it the entire inside wall is wire except maybe the bottom half of the dutch door. Not sure about that. What is the benefit of the dutch door? Wouldn't it be simpler to make a single door? Where you are, as long as you can make it look good enough for you, you could open up the area under the porch roof to really get a ventilation boost. The porch will keep out rain.
I'd move the clean out door out from under the end of the roost and out it in the middle of that run wall next to the pop door. I think that will make clean out easier as you are not working in a corner plus you don't have to worry about removing roosts or hinging the droppings board. Plus that gives you a people door from the coop to the run. I think you will find a people door there really convenient. If you do put the clean-out door where you show, make that the top roost so you only have to remove that one to gain access to the run.
There is a lot or personal preference in what I wrote but some of that comes from experience. I've tried to read everything but probably missed some things. You have put a lot of thought and effort into this, it really looks good.