The idea of iCloud Music Library is that you don’t have to sync, as the library is retrieved for the internet every time you access it, regardless of device. Apple Music downloads for offline use, then have to be selected in the library and downloaded on the device itself directly.
Access your music collection on all of your devices with Apple Music - Apple Support
Add and download music and video content from the Apple Music catalog - Apple Support
When you set up Apple Music on your Mac, you would have made a choice to keep the local copy or not (for pre-existing music). If you did not keep the local copy, then only the iCloud copy exists. The Apple Music iCloud version is DRM-protected and can’t be synced the old way.
To re-download purchases from the iTunes Store, see here:
Redownload apps, music, movies, TV shows, and books from the App Store, iTunes Store, and Apple Books - Apple Support