In principle, not all inverters can directly support a home battery. Home batteries often work with inverters specifically designed to support them, such as hybrid inverters. These inverters have the necessary functionality and communication protocols to communicate with home battery systems.
If you already have an inverter installed and you are considering adding a home battery, it is best to check if your specific inverter is compatible with the type of home battery you want to install. Some home battery system manufacturers offer compatibility lists showing which inverters will work with their systems. If you are unsure, it is best to speak to a qualified solar energy system installer to discuss your options and ensure you choose the right components for your specific situation.