What you are seeing is not that unusual, especially in wet weather. I think it will help you a lot if you know what cocci (or coccidiosis) really is. It can be managed.
Cocci is caused by the numbers of a certain bug (a protozoa) getting out of hand in the chicken’s digestive system. There are different varieties of that bug with different varieties living in different parts of the system. Some are more deadly than others. Some cause bleeding, some don’t.
It’s OK for a few of these bugs to be in the chicken’s system. After two to three weeks the chicken will develop an immunity to that specific strain of cocci, though that does not give immunity against different strains. It’s when the number of the bugs gets too big that it causes problems. You have to guard against that until they develop immunity.
The bug lays eggs (oocysts) that can get passed out of the system through the rear end with the poop. That bug thrives in wet poopy soil or poopy water. After spending a couple of days in wet poopy dirt or poopy water, that egg will hatch inside the chicken if it is eaten. That’s normally how the numbers get out of hand, the chicken is eating wet poopy dirt or drinking poopy water with these bugs in it. Some bugs are stronger than others because of which part of the chicken’s digestive system that strain attacks, but normally you can keep the number under control if you can keep things pretty dry and always give them clean water. Normally but not always.
That bug is not in the air, it is in the dirt. Although your older chickens are immune, that bug still lives in the adults’ intestines. Once your flock has it they always have it and can give it to other chickens.
So how can you manage it? Keep the brooder, coop, and run pretty dry. You should be able to manage that with your brooder OK and probably the coop too. The run or just the outside if they free range can be next to impossible with a run of any size if it sets in raining like it has been for most of us. You just can’t avoid it, but do the best you can. Make sure they are not drinking dirty water. There are a lot of different ways to water them. If you are using something they can poop in or scratch dirt or poopy trash in, chance it out every day. Don’t just add water if it runs low, dump it out and add fresh water. That will keep the mosquito larva from developing too. Another risk is that the watering system might leak and get the bottom of the brooder or coop wet, even if you are using a system where they cannot get the water dirty. You don’t have to keep them absolutely powder dry but the drier it is the less that bug can multiply.
You need to let them develop immunity. It takes two to three weeks after they have been introduced to that bug for them to develop that immunity and they need constant exposure to the bug over that time. They cannot develop that immunity until they are introduced to that bug. They can’t get constant exposure to it if the brooder is powder dry. When one chick gets the bug it passes it to its brooder mates by them eating its poop, but that bug cannot develop enough for it to hatch inside them if the brooder is too dry. If your brooder is too wet, it becomes dangerous. I overcome that problem by feeding them dirt from the run where the adult chickens are every three or four days so they have a constant supply of that bug, but in limited numbers. And I keep the brooder pretty dry.
Some people feed a Chick Starter feed medicated with Amprolium. The dosage in medicated feed is not high enough to kill all the bugs in the chicken’s system but it does limit how many can reproduce. It helps keep the number of bugs under control while allowing enough to reproduce for them to get immunity. A wet brooder, coop, or run is still a danger, then numbers can get out of control even if you are feeding medicated feed. Your adults will not be eating that medicated feed so nothing is stopping them from producing a large number of bugs that can thrive in a wet run. Medicated feed can be really useful in keeping the number under control but it does not excuse a wet brooder. They can still get sick if they are eating medicated feed if the bug is strong enough or if they are in a wet brooder, coop, or run.
There are a couple of myths on this forum about medicated feed. Medicated feed does not give them immunity by itself. It allows them to develop immunity only if they are exposed to the bug. If they are not exposed to that bug they cannot develop immunity. Medicated feed will not cure cocci. The dosage of Amprolium in medicated feed is not strong enough for that. It is more of a partial preventative. If you have an outbreak you need to treat that outbreak.
What happens way to often on this forum is that the chicks are raised in a sterile environment in the brooder, never being exposed to anything. They are never given a chance to develop the immunities they need. They may or may not be given medicated feed while in the brooder. In either case, when they are introduced to the flock they are suddenly exposed to anything the flock has, cocci or something else. Their immunity system is not strong enough to handle that and they get sick, even die. That is what I think is happening to yours. It may not be cocci, the adults may have developed a flock immunity to something else, but it sure sounds like cocci.
I don’t know what your brooder/coop/run system is. My brooder is in the coop so they are exposed to a lot that the adults have anyway but it’s elevated so I have to introduce dirt from the run to them myself so they can work on building up their immune system. When I release them to mingle with the flock they can handle it.
As long as they have had time to develop the immunities they need, age is not very important to this. A chick raised by a broody hen is exposed to all this as soon as they come off the nest and start eating what Mama tells them to eat. These can get cocci if the water is dirty or the run is extremely wet, but normally a broody hen takes them to drier places if she can. Chicks raised with the flock by a broody hen very seldom have any problems with cocci. I integrate my brooder-raised chicks at 5 to 8 weeks old, depending in various things, and they don’t get sick when introduced to the adults. It’s not an age thing though they are normally better able to develop most immunities when they are young.
Hopefully you can get some ideas out of this on how better to manage your system of raising chicks. We are all different and do things different ways. Even if you do all this it is still possible for them to get cocci. You need to be on the lookout for symptoms and be ready to treat at the first sign. It can kill pretty quickly.
Good luck!