FYI: Incorrect Mac behavior when updating an iPhone 11 – could not restore after failed update

Background: MacBook Pro, Monterey 12.2.1; attempting update to iOS 15.3.1 on iPhone-11. (i.e. "all most-recent")

Incident Status: Resolved.

Summary: Incorrect Macintosh Behavior

I backed up my phone to my Mac as I always do, and it offered an update. I said "okay" and went to bed. Next morning, it said "the update failed due to an unknown error," and the phone was in recovery mode (screen showing a lightning cable pointed at a mac). (I don't know if this is the right term: I use the term "recovery mode" here to describe the screen that I saw on the phone, which didn't offer me any options. A lightning cable pointing at a laptop Mac with a "support.apple.com/iphone/restore" message at the top.)

Incorrect Mac Behavior: I restarted the phone and attached it to the Mac (again).

1. On the Finder screen I saw a single word "Loading..." followed by a twirly-icon. No graphics.
2. After about a minute screen turned to a darker shade of grey and I saw: "Software: loading..." Again no graphics. And, the iPhone did not change from recovery mode or show any sort of progress bar.
3. After a minute or so later, the phone briefly flipped to the Apple logo (about 1 second) and back to recovery mode. The finder switched away from the phone.
4. Rinse and repeat ...
5. I do not know if the reason why the update originally failed is because of the status of the Mac. (See below.)

The resolution, such as it was, turned out to be to restart the MacBook. When I did this, suddenly the behavior and the screens was what I had originally expected, and I was able to update the phone, which was otherwise unharmed. I also now did see the expected "Apple logo and progress bar" on the iPhone as this update took place. Suddenly, everything was now working as it should.

I hadn't noticed any unusual behavior from the MacBook, and so it never occurred to me to restart it.

I had called Apple support, so I asked to escalate the incident to "David," who agreed to open an internal trouble ticket (on RADAR ...) documenting this obviously erroneous [Mac ...] behavior that I saw before the restart, so that the engineering teams would know that it had happened. But I also want to document it here on the public discussion system, in case this happens to anyone else.