macOS Monterey: "The selected device could not be found" when connecting iPhone
Ever since updating to macOS 12.0.1, my M1 Mac mini is unable to connect to my iPhone 12 Mini in order to sync my iTunes playlists. Photos and Final Cut both recognize the device and are able to import photos and videos, but Finder and Music.app see the phone but after about 5 minutes they time out with the message "The selected device could not be found." As a result I cannot sync my playlists anymore, nor is my iPhone backed up.
I've rebooted both devices repeatedly, and both have been kept completely up-to-date with the available OS updates. The Mac is running macOS 12.0.1 (21A559) and the iPhone is running iOS 15.1.1 (19B81).
How can I get my dang iPhone to sync music again?