The study of human behavior is more difficult to measure, but can absolutely be held to scientific rigor. In fact, all branches of science have some degree of overlap and interconnection, and thus have blurrier lines than you might expect.

Absolutely, yes.

The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental validation.

Any observable phenomenon should be studied using the scientific method. The alternatives are superstition or ignorance.

Psychology is a good example. It has been limited by our technology and our morals. The human brain is extremely complicated, and we cannot just disrupt peoples lives to create ideal testing conditions. But that doesn't mean that psychology is not science. It just means that it has unique challenges.

If you refuse to consider anything other than randomized control trials science, then you believe we don't have proof that smoking causes cancer.

Yes. "Hard" sciences aren't as perfectly objective like TV would have one believe. Plenty of hard sciences are affected by the replication crisis, like geology and astronomy where one can't set up controlled experiments, same as soft sciences. All of them should strive to develop the best model, break the model, improve the model, repeat.

There are lots of scientific groups that work in the so called soft sciences that apply the usual methods of the hard sciences. It's not about soft or hard, it's about good or bad.

It's not about hardness it's about how you use it

Does it really matter whar we call it?

Well economics damn well shouldn't.