I have a home storage unit and would like it not to provide any power when the wallbox is controlled. If the sun alone is not enough, then the electricity should be taken from the grid. Is that possible?

Unfortunately not. We would have to take over the control of your storage system / inverter. However, we only receive information from these components and then control the wallbox. Your battery storage system will therefore first try to compensate for the missing power, and only when the storage system is empty will electricity be drawn from the grid.