Most of the balcony solar packages already include what you need. They include a battery and on that battery is a receptacle that will supply power if there is no mains. The dogtail that you insert into your house outlet only supplies power if there is mains, but the receptacle on the battery supplies power regardless.

So when the power goes out you unplug your fridge from the wall and plug it into the battery. In essence it operates like the standard camping battery/"solar generator", a la Jackery et al.

To gp’s point, if you’re going through it all just implement it at your panel/subpanel. Mine does auto switch over to power the entire panel and I only know about it from an app notification. Then I can decide if and where I want to power down usage in the house to conserve battery.

Having to plug in individual appliances seems to defeat the entire purpose. What happens if you’re away on holiday? Come home to a fridge full of trash? If power is back, do you even know how long the outage lasted? What about other devices that generally should have nonstop power or are typically hardwired? Sump pumps, HVAC equipment, water heaters, etc.