These vectors are not based in spacetime but in a 2D Hilbert space. Despite adding two more dimensions we have to put them a bit "off to the side" when counting dimensions. Hilbert space does not live in spacetime, but rather gives us "room" to create new dimensions to fully express quantities of interest. These dimensions are called "internal spaces."

You don't need to go to fancy spaces and names to see this effect.
It is also the effect which causes much confusion, although I have never seen it included in any textbook or course.
Consider a simple bicycle pedal crank arm.
Draw yourself the chainwheel, pedal and crank with the origin at the pivot.
Now draw in a few force vectors for the force the foot applies to the pedal as the chainwheel rotates.
Note that this applied force varies in both magnitude and direction at different points around the rotation.
Now tell me where those force vectors 'live' and I will tell you the next stage.
Note I have tried drawing all this out for folks in the past and they never 'get it' until they try to draw this for themselves.