In the Shimano E-Cyclist app the message for succesful calibration is "5050", be it ANT+ or BT.
The Edge 1040 shows the same message with the crank connected via ANT+, but via BT I always get the message "-1 N". Repeating the calibration immediately with the app or ANT+ results in "5050" so it's very unlikely to be a problem with the crank.
Therefore I assume it's just an inconsistency within the Edge firmware. It should be changed to "5050" with BT, too.