No need to send it to skydio, the drone's location is available in the app. Not it's coordinates but an interactive display showing the last known position of the drone and yourself. Takes a little walking around and zooming in on the display but once you have it figured out it'll take you right to the drone. Open up the "Find my Skydio" function in the app once the signal is lost.
Supposedly you can connect the phone to the beacon after the drone is lost and this will work. I don't know if that's true but I can attest that if the app is connected to the beacon when the drone goes down it will record the LKP info. When launching, once the phone is connected I mute the screen and stick it in my pocket and use the beacon. It's not like the phone is open to the app the entire time but the app is running.
I've used it 3 times now. I almost always connect the phone to the beacon before flying for this exact reason. I don't want to find out after the fact that turning on the app later doesn't give you LKP, I know it works correctly when the phone is connected the entire time.