no the pet store lied to you. jesus lol pet stores will say anything. iguanas can get 25 lbs heavy and 6 feet long. they are more like dogs than lizards. an iguana could not live in a 4x2ft cage its whole life unless you were torturing it. An iguanas cage needs to be minimum twice as long as the iguana head to tail and as tall and as wide as the iguana. so a 5 foot long adult iguana needs a 10ft x 5ft x 5ft enclosure and thats on the small side, especially if its in there all the time. lots of people free roam their iguanas. My iguana has his own room, and he can walk around the house wherever he wants. he poops in the bathtub, and he goes in the backyard on his own and walks around all day then when he is done he comes to the back door to be let it and then he walks to his room. they are very intelligent and like i said more like dogs than a gecko or bearded dragon.
a baby iguana can live in a smaller cage like the one you pictured but like i said it depends on its size. if the iguana is 2ft head to tail the cage should be 4 ft x 2ft x 2ft minimum.
if you have the iguana in a tank or glass enclosure for now you should move him to the bird cage, glass tanks are way too small for even baby iguanas and they can injure themselves hitting into the glass.
sadly most pet stores do not keep their animals in conditions that best suite the animals but rather the stores budget and profit. margins. most pet stores keep their lizards in cages that are sadly small.
i recommend getting this book if you will own an iguana
https://www.amazon.com/Green-Iguana-Ultimate-Owners-Manual/dp/1883463505
and read up a bit more on them, if you thought they could live in a small tank like that their whole life then you probably need to research iguanas more. they are a very difficult and sometimes violent and dangerous pet. most people who buy iguanas would be better off with a smaller lizard. again they are really like dinosaur dogs.
Someone already suggested http://www.anapsid.org/iguana/index.html But may I also suggest _Green Iguana The Ultimate Owner's Manual_ by James Hatfield. https://smile.amazon.com/dp/1883463505/ref=cm_sw_em_r_mt_dp_VV4ETQ0FHFDZ4H9Y150J
With those two, I've learned how to take care of my igs. I've had Kazi for over 20 years.
Thank you for asking for help. It means you care!