Just wanted to mention that on the SmartThings platform these are two very different questions.
In SmartThings, anything using an Edge Driver is eligible to run local, meaning direct communication between the hub and that device won’t require the cloud. BUT SmartThings is still a largely cloud based system. The architecture assumes that the HUB has an active connection to the internet.
For example, The SmartThings app ALWAYS requires an active connection to the SmartThings cloud, even if it’s on the same local WiFi as the hub. (They didn’t have to design it that way, but they did.)
Some automations also require an active cloud connection, although there’s no documentation on exactly which ones. At one point SmartThings Home Monitor required the cloud even to arm and disarm. But there are other automations that require the cloud as well.
If you want to be able to operate home automation without the internet (with a few exceptions like third party voice control), then SmartThings is not a match to that requirement. There are quite a few competitors to choose from that do run mostly local after initial setup, including Hubitat, Homeseer, Apple HomeKit, Home Assistant, and Ikea Dirigera. But it’s just not how SmartThings was designed.
Here’s the official schematic for the new (2023) architecture.
So the transition to Edge Drivers will automatically bring more local processing to SmartThings, particularly for zwave, Zigbee, and Thread devices, but you don’t really need to worry about it—that will all happen behind the scenes.
But you don’t get the kind of cloudfree operation you get from many of the other platforms.
The main stuff that will run locally for hub connected devices in SmartThings are simple pre-created automations like having a motion sensor trigger a light switch or having a handheld remote control a smart bulb. But nothing through the app, no notifications, nothing that doesn’t communicate through the hub, and not all automations.
it is what it is.