I’m not sure where you live, but I’ve been privy to thousands of rooftop solar installations deployed in the U.S. (New England mostly) and the common case is to have the inverter wired into the circuit panel with a per-circuit or whole house automatic or manual switch, then also grid tied to realize net metering benefits. Very few installs have battery storage (less than 1%, though this is changing rapidly).
With my setup I just need to flick a switch to cut power to the main grid, and my inverter will automatically turn back on. In Japan at least this feature is ubiquitous - I looked at systems from several manufacturers, and all had the ability to generate electricity during an outage.
Only if you have battery storage.
My system does not have battery storage. A storage battery would be considerably better in the event of a power outage, but also would have doubled the cost of the system. My plan is to have another look at batteries when it is time to replace the inverter, and hopefully the cost per kWh will have dropped by then to the point where batteries make more financial sense.
That’s mostly true, but not entirely. SMA (inverter) offers Secure Power Supply on some models, which give you a single 120 Vac outlet that can provide up to 2 kW (about 15 A) assuming there is enough sunlight. If the solar panels are producing less, it can still provide lower amounts of power. For things like charging phones, a small TV, laptop, modem, and router, it should give you power during most daylight hours, regardless of cloud cover, if you have a 6 kWdc array.