You can save photovoltaic storage capacity by using surpluses smartly - for example, in the hot water tank (then the heat pump does not have to start at night for water heating during the sunny months) or in an E-vehicle. The battery storage only needs to be large enough to cover the base load overnight and to balance power peaks during the day with changing light. If there are no special consumers in the house, 6kWh is usually sufficient. Pay attention to the charging and discharging power. Systems differ significantly in this regard. From 4kW, you have a fairly fast system.