Well, this was quite a mess. I tried all the good fixes mentioned, but no love. I tried logging out of all Apple services and syncing, I tried making another iTunes library, no change. However, I did notice something along the way. My Music Library had moved. It was not where it used to be. I finally decided to go nuclear. I installed MacOS over the top of what was already there using Recovery mode. Upon attaching the USB cord, the Mac immediately said I needed to download new software for iPhone 14 to work with this Mac. It did so and installed it. No love. Still hanging on "determining items to sync." Then I went for the iPhone erase, did an iPhone Restore from the Mac (firmware and all) and set up as a new phone, manually, without bringing over any apps or data. Not restore from a backup. Of course my music library was empty, so I imported a CD and synced. Worked! Then I linked to my real music library (which moved) and synced. Worked!
In the end, I think the real problem was my trial subscription to Apple Music, which I cancelled. It moved my music library from a shared folder to my home folder and rearranged the files in the library. Sync troubles seemed to start at about that time.
I have yet to determine how much pain and agony will come from not moving my apps and data over from a backup. I'm afraid the problem will come back if I restore from a backup.
Thank you for all the tips!