iPhone 14 Pro Max is not recognized by my Mac Pro

I had to do a number of things:

1. I attached the iPhone to my Macbook and it said that it had to download software to recognize the iPhone. Now, my Mac Pro said the same thing, but something didn't go right with THAT download. I think that THAT was where the major screw-up occurred. After the download, the iPhone DID work with the Macbook, and the Macbook recognized my iPhone in iTunes.
2. I disconnected the iPhone from the Macbook, and reconnected it to the Mac Pro. With the successful download that happened when connected to the Macbook, my iPhone on the Mac Pro now DID mount on iTunes. It still didn't mount in the Finder sidebar, but as MGoodmanNV noted above, in Catalina 10.15 or later, it mounts on the Finder sidebar, but with any OS older than that it mounts in iTunes.
3. In iTunes, I clicked on the little iPhone icon near the upper left corner. That puts a new iPhone icon at the top of the iTunes sidebar. I was then able to drag whatever I wanted from inside iTunes (e.g. music, movies) onto that iPhone icon.
4. Here comes the least intuitive part (at least for me). You have to locate the downloaded files (or at least movies - I didn't try to transfer tunes) in the Apple TV iPhone app. Click on Library at the bottom of the screen in the Apple TV iPhone app, and you'll find the movies there. You can play them from inside that app.

Hope this helps someone else.

I spent about 45 minutes on the phone to Apple Support, and I resolved the issue. Thanks.

Thanks very much.