SmartThings is in the middle of a major transition to a whole new architecture Where as I understand it almost everything that uses hub connected devices will run locally on your own hub. And there will be some options for running devices on your LAN locally as well. Devices in Integrations that require their own clouds will continue to use their own clouds. And then when we eventually get matter support, assuming that happens, even more stuff will run locally.
So at this point, I think there’s not much reason to worry about what’s running local or not in January 2022, because by March or April it will probably be an entirely different architecture. (Originally the changeover was announced for the end of 2021, but obviously they’ve missed that target and haven’t announced a specific new one yet.) And then if matter happens on schedule this summer, that will be another change probably with yet more local operation.
During the transition, it can be hard to figure out what’s happening. There’s a setting you can use to mark something as running local when in fact it will still be running in the cloud. And code using the new architecture doesn’t always show up correctly in the IDE, so it might be marked as running in the cloud when it’s actually running local. 
So unless you have a very specific reason for needing to know right now, speaking just for myself, personally I would just wait until March or April and see what’s going on then. There’s going to be a replacement for the ID E as well, but we don’t yet know what information it will have available. so just lots of change happening.
Official announcements:
And here’s the discussion thread on matter if you’re interested in those details: