The micro inverter (most of these balcony kits use micro inverters) uses the grid as the reference. Most of these inverters will actually do nothing when the grid goes down. Like, they shut down for safety so you are not back feeding the grid, but even if you had some sort of back feeding isolation going on, they would still do nothing because they don’t have the reference of the grid.

It’s a downside of many grid tied residential systems (even large ones). No grid = no solar.

The Enphase IQ8 series is one of the first mass market micro inverters based systems to have the ability to make its own tiny electric island when the grid goes down. Requires an isolation switch and a relatively power hungry controller to use that feature, though. I looked into them for a balcony solar setup but it would be way overkill to run a full on controller for 800w of solar!

The best way for a small setup is just have a small “solar generator” battery that can take MC4 connectors as input. Prolonged power outage? Unplug the inverter, plug in the battery.