The function of supplying electricity during a grid outage using a battery is most commonly referred to as a backup power function or emergency power function, although additional terms have become more common in recent years. In principle, there are two main options.
Most inverters provide a second output for the loads that should continue running during a power outage. In many cases, the switchover is so fast that manufacturers even advertise an uninterruptible power supply (UPS) function—i.e., in the millisecond range. With this solution, selected circuits in the main distribution board are connected to this backup output. The loads on these circuits are then supplied during a grid outage.
The second option is to disconnect the system from the public grid (grid isolation) in order to supply the entire house with electricity. In most cases, this grid disconnection is carried out automatically using a dedicated switching / isolation device.
Note: In both cases, you are limited by the maximum output power of the system. This determines how many devices can run at the same time.