How does panel shut-off work for emergency responders? Where I live, a solar energy system is required to have a shut off switch. For example, my system has a big red handle mounted on the side of the house. This is important not just for first responders like firefighters but also for linemen repairing downed lines, which are pretty common where I live (a mountainous rural area).

Given that these store-bought panels are being plugged into house AC, it follows that they have built-in inverters. Many grid-tied inverters are “grid follow”, meaning that they adjust themselves to grid frequency/phase. So, just speculating here… maybe the inverter senses when the mains go down and turns itself off? I would love to know from an EE what is actually happening wrt safety.

It'll be the same as larger inverters for roof-top solar - they are constantly monitoring the mains cycle and will shut off if the voltage (or probably frequency too?) goes out of range, let alone drops out entirely. The relevant standards in the UK are G98/G99.

These inverters have to switch off if they cannot detect a grid signal, or if the grid frequency/voltage goes out of the safe range.

Same legislation as the non-plug&play inverters.