I don't know what "hard science" is or what that means, but I do know that academically, economics is categorized as a social science. I've taken several economics courses in college (micro, macro, and "money and banking"), as well as a course called "engineering economics" taught as an engineering course, by an engineering professor, for engineering students. From the sound of it, it doesn't seem to me that a "hard science" is mutually exclusive from a social science.
A social science is simply a science that pertains to human behavior involvement, such as psychology, social and cultural geography, (human) history, political science, etc. It's to distinguish it from natural sciences that (can) exist regardless of human existence (physics, chemistry, astronomy, biology, geology, etc.).
Economics is physics and mathematics; it's what distinguishes a practicing engineer from a practicing scientist (an engineer's job is to do the most with the least (that's what optimization & efficiency are about), which is essentially about mainly or predominantly getting the cost as low as possible for that widget (whereas a scientist's job is practically to beg for the billions of dollars it costs to build that fancy new particle collider).
The only mathematical distinction between economics and physics (other than the human involvement stuff) is that economics uses a dollar sign (or whatever denomination) as part of their calculations. If you remove it, you have mass or energy, and if you're talking about something like a pay rate, you're talking about power (pay rate, or something in units of Joules per second in physics).
The word "work" is literally used to describe the action a person does when they're doing a job, and it's a word that has a specific meaning in physics; depending on the system, it's calculated as energy transfer as a product of force x displacement x angle between the force & displacement direction of an object (linear mechanical), torque x angular displacement (rotational mechanical), isobaric: pressure x change in volume of a gas, heat added to a system - change in internal energy aka 1st law of thermodynamics, electrical: charge x potential difference, gravity: mass x g x height, etc. The bulk of manual labor work done by humans is the mechanical type of systems. They all have the same SI units as energy: J (Joules).
You also mentioned political science & I think I can agree that it also plays a role; in a nutshell, political science is about the use of force on society (as in who, what when, where, how, and why to apply it). Force is also a word that has a specific meaning in physics and is Newton's 2nd law of motion: F=ma (force = mass x acceleration). In the political science sense or context, it's about imposing human restrictions on work (e.g. the work involved in breaking into a shop or car to steal things).
I know there's more to work than manual labor, but the same type of principles apply to white collar jobs.
The operation of the economy can be analyzed and designed, just like any other engineering system, for optimization and efficiency, and that's what's happening when an employer is making a decision about who to hire.
I'm not sure I agree entirely with this assessment, although I can see where you're coming from. I see economics as a social science in that same sense as philosophy, history, political science, sociology, psychology. The hard, or natural, sciences attempt to explain nature, whereas the social sciences delve into the intricacies of human societies and the vagaries and perceptions of the human mind. It is still a science, of course. But it is often a measure of human choices based upon human values, which can often be subjective and irrational.
It is what it is, and these are still useful and necessary fields of study for the benefit of society. However, we're talking about philosophical positions, for the most part. Competing sets of values and ideals. That's really all that it comes down to, whenever these kinds of discussions come up.