The list you’re seeing in Finder isn’t built from a particular folder. It comes from the library in the Music app on your Mac.
Open Music, then use File > Import (or drag the music files into the Music window). Once the songs are in your Music library, their artists/albums should appear in that Finder sync list. Simply putting files somewhere inside your Musicfolder won’t add them to the library.
→ Import music from a computer to Music on Mac - Apple Support
If you want to see where Music is storing its files, go to Music > Settings > Files and check Media Location.
→ Change Files settings in Music on Mac - Apple Support
After importing the new songs, reconnect/select the iPhone in Finder, choose them under Music, and click Apply or Sync.
→ Use the Finder to sync your iPhone, iPad or iPod touch with your Mac – Apple Support