Right now, only the official smartlighting feature and a few bits of smart home monitor can run locally, and then only if they are limited to devices using device type handlers which can run locally. Routines cannot run locally, you cannot arm/disarm smart home monitor locally, and you can’t use the app on the phone locally even if your phone is on the same LAN as your hub.
There’s no official list of the handlers, but there is a community thread of handlers that have been confirmed to run locally. There are several sensors there:
