Traditional sway bar vs heave spring

So I was looking into sway bar setups like a heave spring and was wondering why heave springs operate the way they do.

Now with a traditional sway bar, when the left wheel is compressed, the sway bar will attempt to compress the right wheel.

From what I’ve seen about heave springs is the opposite. When you compress the left wheel, the bell crank and torsion bar will put droop force on the right wheel.

Can anyone explain the theory behind this?

Just to clarify, are you thinking of the heave springs used with a 3 spring setup? Not something I've played with (looked at some and they're as confusing AF, as you've already found), but the theory is to separate wheel motion/control between roll resistance/single wheel bump loads, and simultaneous bump loadings. The intent is to give a better wheel vs chassis balance - consider what happens if you need a high spring rate for chassis control under high aero' loadings and compressive loadings, but that results in the vehicle being too stiff in roll across that axle.

You may wish to look at "Z" bars, and consider what would happen if you put a spring assembly between the bar's mountings and the chassis.