How do I transfer music from Mac to iPhone?

You can transfer purchases from device to computer. Syncing works computer to device, and if it is a new computer with respect to the device there will typically be a prompt that talks about removing any existing content from the device. See if this article is any better: Sync content between your Mac and iPhone, iPad, or iPod touch - Apple Support. In particular if you are using the Music app on a Mac then you need to connect your device to your computer, trust the computer when prompted on the device, and open it in Finder to make sync selections. Your content should be in the Music app before you start.

tt2

See Intro to syncing your Mac and your devices - Apple Support.

tt2