How can I transfer my songs in Music on my Mac Studio M1 to Music in my iPhone 14?

Syncing should not change anything on the Mac.

Syncing songs has not changed since iOS 10.15 Catalina (6 years ago). It's done through the Finder.

click here ➜ Use the Finder to sync your iPhone, iPad, or iPod touch with your Mac - Apple Support

Unless you are

• subscribing to iTunes Match and using "Sync Library"
• subscribing to Apple Music and using "Sync Library"

synchronization is as Phil0124 describes.

It's one-way, from a master library on a Mac or PC, to a mobile device (iPhone, iPad, or iPod). With the exception that if you have bought a song from the iTunes Store on an iPhone, iPad, or iPod touch, you can load it back onto the computer. (In the old days, I think synchronization copied it from the mobile device to the computer; now the model may be that you re-download the song, free of charge, on the computer.)

If you are an Apple Music subscriber and are using "Sync Library", then I believe that copies synchronized through "iCloud Music Library" only work for as long as you are a subscriber. Stop subscribing, and the "original" (e.g., the copies on your Mac Studio) should be OK, but the copies on your iPhone may stop working. (And you may need to do a manual synchronization with no songs selected to clear them out.)

I think you misread or misunderstood the message.

When you sync an iPhone with a computer for the first time, the music on the iPhone is replaced with whatever is on the Mac.

If your Mac did not already have all the music on your iPhone, then the sync would delete everything on the iPhone and replace it with whatever was on the Mac. This is the way syncing has always worked.

As I said before, the music on the Mac will not be altered.