You need to be patient. The phones are still transferring data. I left my old iPhone SE and new iPhone 12 Mini adjacent to each other and both on charger power overnight. I'm not certain how long the last "two minutes" took, but it had already been in that mode for a few hours when I went to bed hoping this was just "normal."
The next morning, viola! All was well. Everything had transferred, including all of my previous phone's settings, screen background, photos, music, everything! Also, the old iPhone had been completely reset to factory settings. Nothing whatsoever remained on it.
Bottomline, be patient.