I had some variation of this.
Unboxing, nice experience. Protective screen application, perfect for once! Setup process, still ongoing for 7+ hours…
Initially things went smoothly, my old 12 Pro Max found the new 16 Pro Max, offered to set it up, the speculous blue orb scan worked, and my AT&T # was activated on the 16 quickly. Like others, though, it hung there, with neither device giving feedback other than the spinning fan circle. I foolishly thought it had started data transfer and let them spin, both devices plugged into power, and went to bed.
I woke up after a few hours and checked on progress, there was none. I found these posts and began trying resolutions. After power cycling both phones, I was back to setup, but the magic blue orb no longer worked. The manual code entry did, and it looked like I was making progress. The new 16 then offered to update it’s software to 18.1 Beta (yes, I’m on the beta program, I realize the risk and that part of this is my fault) and I foolishly accepted. I went back to sleep again.
I awoke a few hours later to find the new phone back at hello and the old spinning at nothing. Another round of power of the old phone to resume, this time manual setup didn’t acknowledge on new phone. A hah!, I said, someone here had success with the phones directly connected (c -> lightning) so I cycled both, still no acknowledgement. I removed direct connection, power cycled both again, and after manual code entry finally got the data transfer initiated!
I eagerly waited for the time remaining progress indicator to show… Time remaining: 7 hours! I plugged both into power again. Within 20 mins this 7 hours was down to current estimate of 2, and I’m hoping it will continue to decrease faster than real time so I can use one of my phones soon.
I debated just starting fresh, but had spent a few hours preparing by deleting old, unused apps and reorganizing them all to my liking. I’m glad I chose to start this at the end of the day when the phones weren’t urgently needed. I’m sure I’ll enjoy the new 16 Pro Max, but this has certainly taken the shine off of my new phone experience.
Thanks to all who posted solutions here. For others experiencing the same, try, try again, and persevere!