Looking at drawings 3 & 4, these linear vs rotational springs are analogous considering they are each at rest in the center of the user control slider. They can act like a spring in either direction, and are basically sitting there in the neutral or non-energy-storing condition (zero-sprung or zero-wound respectively) until you move the slider away from the center position.
Take a look at the 9th or 10th interactive drawing, where you can move the slider to the right to wind the mainspring, then release the slider to watch the mainspring unwind.
When the energy is depleted, all the bands in the coil are bunched up around the outside of the barrel. It's not much of a spring any more.
This is the same type of torsion spring as in drawing 4 but with the mainspring being used for primary energy storage there is no desire for recovery to a neutral position from both clockwise & counterclockwise directions like you see in drawing 4. Instead you only need to ever draw energy from storage to use in a single rotational direction. Opposite rotation is used only to store externally applied energy.
So you wind it in one direction to store energy then it releases the energy in the opposite direction.
But without the precurvature shown in drawing 11 the torsion spring would tend to be exhausted when it was "zero-wound" like the one in drawing 4, with the coils widely spaced away from each other, free to absorb & recover energy from either rotational direction. And since we only need to draw energy in one rotational direction, that amounts to only half of the energy the spring is capable of storing for our purposes. Notice how about half the length of the spring is coiled similarly to drawing 4, with the upper half of the loose spring coiled less tightly and in the opposite direction.
Because when our mainspring is exhausted, we want it to be bunched up along the outside of the barrel so we get the most out of it before it needs to be retensioned. And when it's fully retensioned we want to get maximum energy storage from the hardware so at that starting point we want the coils to be tighly wound, bunched up around the arbor.
But not too tight.
Or it could be overwound.
As long as there is some space in between the coils, when recovering rotational energy you have access to what is stored along the entire length of the free portion of the coil. But once it's wound tightly enough for the coils to be in significant direct concentric contact, the free portion of the coil becomes so small it does not contain enough energy to drive the timekeeping mechanism.
It could get so tight that it's not much of a spring any more. Closer to a solid cylinder with a slight tab hanging off.
Which is more of a problem when both ends of the torsion spring are permanently attached to their substrates.
Instead in these drawings, the color-coded metal strip is used to provide a friction grip between the outer end of the coil and the barrel, strong enough grip to drive the timekeeping mechanism but designed to slip counterclockwise within the barrel if manual winding proceeeds more than necessary, slipping before the coil can get wound too tightly.
Basically, overcharge protection for a non-electric hardware device.