The app and car communicate directly over Bluetooth for a number of functions, like lock/unlock, popping the trunk, and starting the car. This outage didn’t affect that (I drove my Model 3 during this time period).

You can start the car over the internet, too, but this is not typical, and the app actually warns you when you try to to do this.

Finally, the Model 3/Y have backup keycards that Tesla encourages you to keep with you just in case your phone dies. The app tells you this when you first pair your phone.