Why won't my iPhone 16 show in iTunes on iMac?

What versions of macOS and of iTunes are you running? (If you are syncing to the machine listed in your tag line, the one running Ventura, that one wouldn't be able to run iTunes. You would set up your libraries using the Music and TV applications, and then sync using the Finder.)

Sync content between your Mac and iPhone, iPad, or iPod touch - Apple Support

For an iPhone 16 running iOS 18,

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Syncing to a Mac or PC requires:

• macOS Catalina 10.15 or later using the Finder
• macOS High Sierra 10.13 through macOS Mojave 10.14.6 using iTunes 12.8 or later
• Windows 10 or later using iTunes 12.12.10 or later (free download from apple.com/itunes/download)

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Note how syncing from Macs running El Capitan or Sierra is no longer supported. Also, while syncing from a Mac running High Sierra is theoretically supported, you will find lots of reports in these forums of people who have had trouble syncing iPhones running iOS 17, or later, with Macs running High Sierra.

iTunes for Mac was replaced by the Music app with the launch of macOS Catalina in 2019.

Undoubtedly your obsolete iTunes cannot possibly support an iOS 18 iPhone.