That’s mostly true, Although a little by little overtime they have been trying to move more rules processing to the hub.
At first it was just the rules created through “smartlighting“ and then only some of those.
Then they added some of the rules created through the security wizard, at that time called “smart home monitor“, but then they took those away again and moved them back to the cloud when the security wizard was changed to “smartthings home monitor.“
Most recently they been trying to move some of the “rules API“ for the newest architecture to the hub. It’s not quite clear exactly what’s eligible for this, but that’s why there is now a cloud/local icon on the automations.
They keep promising more local processing, but it’s still primarily a cloud-based system.
There are a number of competitors, including Hubitat, Homeseer, and Apple’s HomeKit, which do run everything locally except for integrations with third-party cloud-based systems like voice assistants. But with SmartThings A lot of stuff still runs in the cloud.
And ST still makes a lot of changes to the cloud platform which are neither documented nor announced in advance, which is why there are so many threads in the forum along the lines of “everything’s been running fine for months and now suddenly things have changed. What happened?”
It’s not clear to me what will happen once smartthings adds matter support. Matter on Apple will be able to run locally for many devices, but the same devices might require a cloud to run on smartthings.
We already see that with Wi-Fi devices like Meross. The same smart plug can run locally on HomeKit, no cloud required except for voice control, but requires an active Internet connection to run with smartthings. So that might continue once matter support arrives, we just don’t know.