Balcony solar does send excess power back to the grid. If you have a really old electricity meter it might count backwards when that happens and you might be legally required to get it replaced before installing the panels (depending on local laws).

A battery that sends power directly to your entire household but never back to the larger grid would require integration with your electricity meter (not just plugging it into a random outlet) because you can't measure the electricity usage in your home from a random outlet and know when to discharge.