I love the idea of local only apps woth no network comms. I do wish macOS had some way you could enforce that out of the box though. Rather than trust the claims of the developer.
Another app I love that does the same. Queryable which lets you natural language search your photos on device on iOS and predates most of the current AI craze (2022) and also apple adding this themselves to photos: https://queryable.app/
Indeed, macOS only blocks incoming traffic. For this app and in "local mode", there are only two kinds of requests: one to download the models from HF and an optional version check that sends nothing about the user and can be turned off. A simple test, once you download, try turning off your wifi and use the app.
Little snitch is the best solution for firewalling off applications from the network