If it’s using an edge driver, it is running locally.
If you are looking at the IDE, that’s designed for the old architecture, and the information there on devices using edge drivers is often both inaccurate and incomplete. So it’s really not a very useful source of information anymore, except to get some old parameters and device details.
If when you open the SmartThings app the device indicates that it’s using a driver, then it’s local. 
See point 3 in the community FAQ:
FAQ: I have no idea what Edge is. Is that a new developer tool? (2022)