I've googled the heck out this (as a non-physicist) and found a ton of similar questions answered but did not find anything that made the light bulb go on. I don't think I'm a crank, so here it goes.
When one object exerts a force an another and they do not move, the net force is zero. I agree. But intuitively there must be non-zero forces somewhere in this system (if not what do we call these "energies"?). To the observer, however, there doesn't appear to be any non-zero force in any component of the system because there's no acceleration to be found. In other words, one might think: I don't see motion anywhere, so there's definitely no acceleration, so definitely there's no force. But that doesn't line up with reality and intuition, in which we know some sort of energy interaction is taking place.
I put my back up against a brick wall of a building. I'm poised to push to push the wall but have not begun to exert myself. I'm at rest and static. Then, after a few seconds I begin to push. While I'm pushing/exerting let's assume that there's no movement visible from a macro-observer level of my posture or body when I transition from non-exertion to exertion. Let's also assume that I'm pushing perfectly perpendicularly to the wall and that the wall cannot be moved by my puny legs. The net force is zero. No argument. But there's no acceleration to be found anywhere that the eye can see. The wall has not moved, I have not moved. If you need a more ideal pusher please feel free to replace my body with whatever.
Clearly energy is being expended somewhere here. I figure that either there's some other energy exchange going— one that's not considered force in the $F = ma$ sense. Or maybe that we're now talking about how force is transformed into something chemical or some material phenomenon of my pushing body and the brick wall.
Why I need another perspective
I've spent decent time googling this. I've read several responses to similar questions in which the responders talk say things like "no! $F = ma = 0$ means net force of zero" — okay, I get it, I agree with it, but I don't see any non-zero non-net forces here either, because I haven't observed any acceleration in any component of the system. If the net force is the vector sum of all the vector forces then where are these vector forces with non zero accelerations (assuming there's a non-zero force somewhere)?
The selected answer here for example is not satisfying to me. https://physics.stackexchange.com/a/19401/271396
For all those who make an effort to understand where my density lies, thank you!