There are no key fobs on the market that work using Bluetooth. They use common RF bands, and the "passive entry fobs" communicate through challenge response. The car MUST have radio transmitters and receivers capable of sending RF challenges when the handle is pressed, so the key fob can send the response. The car's multiple RF receivers MUST be able to use signal strength and triangulation to determine if the key fob is on the driver side door, passenger, rear, or inside.
Notice, the car needs to have specific hardware that the Model 3 simply wasn't designed for.
This new key fob would be the first Bluetooth key fob in the market. And it is Bluetooth LE per the FCC application.
Passive RF key fobs, like we are all used to... are VERY low power. They sit listening only, no beacons, no heavy protocols, etc. Much lower power requirements than even Bluetooth Low Energy. A phone is charged everyday, but a fob must last for months if not years.
So this key fob is more of a workaround. It has to use Bluetooth, because the car's hardware doesn't transmit or receive on any other frequencies or protocols. And BLE still requires too much power if active all the time, as it would need to be in a "passive entry" mode. Even a BT beacon interval of 5 seconds would drain the battery too fast, and though 1 minute intervals might save the battery, it won't work walking up to a car.
So, it must use Bluetooth only when the button is pressed.