It does transfer, but you have to accept a request to do it. I just can’t remember if that request was on my phone or my watch 😂 thought it has been 3 weeks since.The Quick Transfer process does NOT transfer Apple Watch from old iPhone to new.
When I did my transfer from XS to iPhone 12, everything transferred over other than my S4 Watch. I had to then unpair the watch from the XS and repair it to the iPhone 12 (you can’t have a watch paired to more than one iPhone at a time) but once I repaired, all the Apple Watch data from old phone to new was brought over (it kept all my historic workouts and everything).
The process of unpairing the watch from an old iPhone actually creates a backup of the watch. When you then repair it to the new iPhone, you just opt to ‘Restore from Back up’ instead of ‘Set up as new Watch’.
I had the notification when moving from XR to 12 Pro and it worked perfectly.