Turns out it was all easy, except . . . see below.
I just put the new 16 Pro next to the 13 Mini and went through the automatic transfer. That took less than an hour, plus a couple of hours for all the apps to download. During the app downloading, I was able to use the phone to set up the eSim.
Then I went to Tracfone and activated the first eSim as a new phone, picking up the number from the 13 Mini with its SIM card. That worked well, too. A first for Tracfone, in my experience. Maybe that was because it was all online and without having to deal with any tracfone (non)support person.
Then I updated the new phone from iOS 18 to 18.2. That was pretty quick, even though my internet is only around 9 Mbps download.
Of course, there were lots of apps (not all) requiring me to login again once.
What didn't work was any transfer of my email. On my old phone, I have many thousands going back years. I use POP3. I still have them on my old phone and my laptop, but they did not transfer to my new phone. In past iPhone upgrades, the emails always did transfer. Right now, the only emails on my new phone are the most recent week, which were still on the POP3 server.
I also had an archive folder on my old phone. That's gone, too. It probably had 5,000+ emails in it.
The question is, are they really just not ever going to show, or are they somehow hidden? Maybe it has something to do with my old phone having iOS 17 and the new one having iOS 18? Any advice about this would be appreciated.