I had the same problem and followed the path with installing without backup, updating iOS, resetting the phone and then retry starting over. I did not make it past emergency screen again (direct transfer or from cloud gave same non-response). Plenty of forced resets along the way. Talked to support - they set up a call today with senior adviser to help solve the problem- went to bed frustrated.
After some sleep I decided to try something else: Bypass my Wi-Fi mesh with Eeroplus, just connect to WI-FI directly. So another reset, but it worked for me, direct transfer is completed.
In retrospect, not clear whether all the other stuff was ever needed; certainly bypassing eeroplus is simpler to try first. I made sure both devices hook up to the same non-Eeroplus wifi when doing this. The call with support will be brief.