If you can do your best to make sure they have enough room and aren’t crowded - the more space they have the better, but there’s many creative ways to accomplish this. You don’t need to have a chicken mansion (although I wish I had one). As
@LateBirdFarms said, even letting them out earlier perhaps. Or removing a nesting box - I think you have 2?
Also, try to get some chicken food as soon as you can. Making your own food is complicated, but perhaps you can research that option after your birds are integrated if you’d like.
If you do these things it may make it easier to integrate the new chickens successfully.