Seems an odd one, it is supposed to act in the way you first mentioned, where the L3 would act as the reciever.
To be openly honest though, the bugs with various transfer apps is why I just do it manually with SD card.
The only one that seemed to work well enough for me was the in built android one that was toned down after Oreo in favour of 3rd party manufacturer apps that always seemed to miss this or not include that..
Try starting the xperia transfer on the opposite device and see if that kicks the correct identifiers into place