iPhone 13 not syncing with MacBook Pro, prompted to reset

"iPhone 13 not syncing with MacBook Pro, prompted to reset: [...]I haven't been able to sync my iPhone with my MacBook Pro. I keep getting a call to Reset the phone. I have things backed up to the Cloud, but I'm nervous about doing a full Reset, or if that will even solve my issue.[...]"

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iPhone 13 and Monterey Mac:

Try an Update Through a Computer. That would make this pairing begin, as a trusted device connection. In your iPhone and macOS, do so using Finder. Go Here: Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

See my User Tip: Updating your iOS Device Through a Computer: - User Tip

“The contents of the iPhone “iPhone” could not be read. Click Restore to restore this iPhone to factory settings.”

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Upgrade the macOS, or the Mac:

That message would indicate that your macOS is so obsolete that it is not able to match those of more-modern devices operability. So, you'll need to use a more-modern macOS. This all comes to getting this to sync. This restore it is mentioning to you about is required for the iPhone to operate with an older macOS. So, take this a good reason to upgrade your Mac.

"BTW: My ultimate goal here is to get my iTunes Library on the MacBook Pro synced with my iTunes on my iPhone."

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Accessing iTunes Library Across your Devices:

Do you have an Apple One Subscription? Having one, your items (including home music) will sync across all devices assigned to your Apple Account. Go Here: Apple One - Apple