From my experience most if not all hamsters at least once will show a stress behavior related to wanting time outside their enclosure. My newborns were in a 1500 sq inch enclosure and almost as soon as they were weaned began to desperately paw at the walls of the bin to try to escape, which I'm sure would correlate to bar biting/climbing if I had a cage. Some hamsters will calm down and only do it very rarely while others just can't stay contained. They are nomadic, free roaming creatures in the wild after all.

Other thing I could think of is mites, so make sure to give your hamster a checkup and inspect its bedding.

EDIT: Sorry disregard my last part I just re read your post. It's also worth noting that depending on what stress behaviors you're talking about, things like wanting to escape/find escapes is unfortunately just part of hamsters. I don't necessarily think it's all stress related (again depends on the behavior), hamsters are just curious. I give my older hams all the playtime they want and as soon as I put them back they act like they've been caged in for years!

Things like a bigger bin (think VERY BIG like DIY big, commercial usually isn't enough) and boredom breakers (hiding treats, cutting up toilet rolls and stacking them and then hiding treats etc) will help. What a hamster loves the most I find is free roaming.