Many smart home accessories rely on cloud servers to process commands, so when the internet goes down they can stop responding or stay stuck in their last state. That is mostly a nuisance, but for security cameras, thermostats, or health-related devices it can become a real problem.
A more reliable approach is to build your setup around a local hub. Hubs can still connect to the internet, but they store and run automations on their own as long as they have power. Matter-enabled speakers and displays can technically do this too, though in practice Amazon and Google rarely take advantage of it. The most robust hubs use mesh radio standards like Thread, Zigbee, or Z-Wave, which let many devices connect without relying on Wi-Fi.
Power is the other half of the equation. Whole-home battery systems are too expensive for most people, so the article suggests choosing individual devices with built-in redundancy. For example, some smart lamps have batteries that keep them working during a power cut, and smart thermostats will hold their last schedule as long as the HVAC system has power. For security systems, cellular backup is worth considering if outages are common in your area.