Is it traumatic for birds to change cages?

it can depend on the bird. you could just swap cages but the bird could become very stressed and not eat/sleep properly. it's best to gradually change the cages.

let the bird have both cages. sleeping in the old one at night. and having the new one sit next to it. during the day allow the bird to travel between both cages at it's leisure so it gets used to the new one.

when it seems ok with the new one place it in that cage at night but keep the old one beside it. when it seems happy with the change you should be find to remove the ld one entirely.

i really hope this helps. just be sure that your bird stays happy and eats enough and it should be fine.