Unless you're
- an iTunes Match subscriber, or
- an Apple Music subscriber who has the "Sync Library" feature turned on (I prefer to keep it turned off)
the way that you get purchased music from a Mac to an iPhone is through manual synchronization. You load your music into your Mac's iTunes library or Music library. Then you use a cable to connect your iPhone to your Mac – and use iTunes or the Finder to select which tracks to load onto the iPhone.
Sync content between your Mac and iPhone, iPad, or iPod touch - Apple Support
You can synchronize your iPhone to one computer at a time – and it's a one-way sync (from computer to phone; no using the phone to copy music from one computer to another). That dates back to the way the original iPod music player worked.
There is no need to manually synchronize photos in order to manually synchronize music, music ivideos, TV shows, and Digital Copies of Hollywood movies. I synchronize music manually, and photos using iCloud Photos.