I want playlist changes to show up in the Music library

Not really, but a simple way to do what you're probably wanting to do is:

Go into your playlist, select all the songs in it using the Command, A keycommand, or choosing Edit (from the menu) -- Select All.

Then you can get info on the songs you have selected by going to the File menu --> Get info, and make changes that affect all the songs, such as the song album or artist name, genre, etc.

If you don't want to apply it to ALL the songs, then simply select a portion of the songs to affect and then click Get info.

Yes, the get info changes you do on a group of songs from anywhere in iTunes will change them on the files themselves, thus also in your main music library.

All songs are in the library.

A playlist is simply a link to a song in the library.

When you make a change to a song in a playlist you are making a change to the song in the library.

Likewise, when you make a change to a song in the library, it will show up in the playlist.