you are exactly right!
One end of the springs generated by the elastic support is fixed in space and the other end is attached to a node of the assigned entity. Each node gets one spring. In total they represent the given spring stiffness with local stiffnesses correctly distributed.
As you said, in your example adding elastic support springs would not work. The model would basically behave as if the lower part would not exist.
This would actually need spring connectors, you can directly create a feature request in our vote for features category.
If you don’t want to model the actual spring, with the current capabilities, I would create a simple surrogate model, basically a beam and modify material parameters such that it represents the compression stiffness of the spring correctly (up to a certain degree). If you have also torsion and bending moments, this might actually not work.