Music transfer incomplete on iPhone 17, seeking sync guidance

Bought new iPhone 17 at Apple Store, which kindly made a temporary iCloud backup of my old phone to expedite an on-the-spot data transfer. The old phone had some 2,000 songs on it, backed up and synced with my iMac at home. (None of my music is in the Cloud.) Only after leaving the store did I realize that the data transfer was incomplete with respect to the music. Many playlists and individual titles are grayed out or missing the artwork, and some of them, when I try to play them, display an error message "This item is not currently available in your country or region," which is patently ridiculous because they are bought and paid for, and play perfectly from my hard drive (and, indeed, from thee old iPhone, which I still have). I'm hoping that a routine sync with a USB cable will clean up the new iPhone and match its music archive with what's on the hard drive, but I'm reluctant to dive in without a little guidance: what are the chances that thee iPhone will overwrite what's on the Mac?