I'd argue that the state is any man or woman who represents themselves as that entity and exercises authority under that mantle. Whether it's a junior sergeant or the Chief of Staff of the Army, they're all the state. The state is a collection of individuals operating through an authoritarian framework. You're right that there is no "the state" as a physical entity, but it exists in the way a corporation exists; a group of people, operating under a set of rules, for a particular purpose. In the case of the state, it's to monopolize decision-making through force over a particular geographical area.
I'm glad you brought up being in an actual firefight. I think we're on the same page as far as shoulder the moral burden, which is what I was getting at it in some many words. Whether it's a war or not, you are ultimately responsible for the killing you do. I'm not suggesting soldiers should be pacifists, but it is a delusion to pretend that war magically erases any moral culpability. It doesn't. I'd argue that if you come to this conclusion and you're in, you should get out. That's what I did, and I think anyone who honestly calculates the moral burden of killing another human being on the order of their superior would feel the same way.
It's the same argument for doctors who apply vaccines they know are unsafe, truck drivers who take pigs to the slaughterhouse, landscapers spraying pesticides on school yards, the maintenance guy who disables the fire alarm so it doesn't go off accidentally; a whole lot of people in general. It just keeps going and going.
The secretary who serves coffee to politicians is technically the state. She exercises authority in her range of tasks.
Except the state is something very specific: the group of people seeking to monopolize decision-making by force over a geographical area. Truck drivers don't do that. Doctors applying vaccines aren't in that category. The maintenance guy isn't that. Neither are the landscapers. In whatever capacity they are liable for their actions, they're not the state.
The secretary serving coffee is technically the state. You're correct. She is employed by that group of people and works, in whatever small way, to facilitate their goal.
That's state's a specific organization, boss. It's not a physical thing, but it is a group of people that can be identified and categorized.