Unless something has changed, the current local processing is limited to the official smart lighting feature and a few parts of Smart Home Monitor.
No custom code runs locally.
Modes cannot be changed locally.
The Security features cannot be armed/disarmed locally.
Smart locks cannot be opened locally via automation with the new app.
The mobile app cannot communicate with the hub locally.
New automations cannot be added locally even if they would run locally once they were added.
Scenes do not run locally.
Notifications do not run locally.
So if you have predefined some automations that will not require location.mode changes or security.mode changes and you don’t need to do anything in the mobile app and you don’t need notifications and you aren’t using scenes and you don’t need ST to unlock the doors then, OK, some stuff will run locally. Otherwise you’re out of luck.
I suppose that’s technically greater than 0 but it’s not anything like the use cases advertised on the box or the website.