Migrating to a new iPhone using encrypted backup to a Mac

Here is an exchange I had on a groups.io iPhone forum about Migrating to a new iPhone using encrypted backup to a Mac.

I would welcome anyone confirming that I am right or pointing out that I am wrong.

Another poster agreeing with me noted this:

Whether I set up new iPhones or iPads from encrypted backups on my iMac or from iCloud backups, all the third-party app icons appear on the new device and then take some time to download.  I’ve never had to go to the App Store to re-download any of them.

My response was:

That is precisely what happened when, about three weeks ago, I got a refurbished iPhone 13 Pro Max.

I did a final, encrypted backup of my iPhone Xs Max, in Finder, to my 2002 iMac running Ventura, attached the new iPhone 13, and everything moved from that encrypted backup to my new 13.  The only extra step I had to take was to enter the security codes for the credit cards I had in my Apple Wallet.

When my wife tried exactly the same thing a few days ago on her 2019 MB Pro running Ventura, it flopped, transferring only her Apple Apps and none of her third party apps. She had to start over and use Quick Start which worked in that it moved everything from her iPhone X to her new iPhone 13 Pro

I have no idea why it worked perfectly for me and flopped for my wife...but it did work for me and some contributors to that thread claim what I did is not possible.