Add A Column called "Playlist" to my Music library

At this point, I don't think there is an option for you to do that with Apple Music.

While in the Library, right-click on the top portion of the song listings and select what columns you want to show.

There isn't an option that says "Playlist" or anything remote to that that would show you the playlist that a song is a part of. Yes, that would be a great idea, but I don't think Apple has yet to implement that.

MTR Plato,

The available capability is to right-click a song and choose "Show in Playlist." It shows a list of all the playlists the song is in. If that playlist is in a folder, it will show the structure. (If the song is in no playlists, the menu item will not appear.)