Apple Music - can't add songs to existing playlist

Sorry that hasn't worked for you.

Am not sure why you get an error message:

Thank you to turingtest2 for joining the discussion, and providing expert info.

Perhaps this article puts it a little differently:

How to make a playlist in the Apple Music app - Apple Support

says:

Create a playlist on your Mac or PC

1. 1. Open the Apple Music app or iTunes.
   2. In the menu bar, choose File > New > Playlist.
   3. Give your playlist a name.
   4. Drag and drop music to your playlist in the sidebar.

Want to add music to an existing playlist?

Just drag and drop music to a playlist in the sidebar.

Hi MartaTZ

Welcome to the Apple Community.

Re: "I've created a new playlist on my Mac, but I can't add any songs"

Apple support have an article online(link below) that may help:.

How to: Create, edit and delete playlists in Music on Mac – Apple Support

Eg: says:

To add items to a playlist, do any of the following:

✽ From anywhere in your music library, drag an item to a playlist in the sidebar.

or

✽ Control-click an item, choose Add to Playlist, then choose a playlist (or use the Touch Bar).

Tip: To add songs to a playlist without adding them to your library,

✽ choose Music > Settings, click Advanced,

✽ then unselect “Add songs to Library when adding to playlists”.

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More info:

How to build your music library of songs and albums.

Get started by adding music to Music on Mac – Apple Support

How to see which playlists have a particular song or item in them.

See which Music playlists a song is in on Mac – Apple Support

Create, edit, and delete Smart Playlists in Music on Mac

In Music on Mac, create a Smart Playlist—a playlist that meets your specific criteria. 

Music adds songs to the playlist automatically....

Create, edit and delete Smart Playlists in Music on Mac – Apple Support

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Resource:

Apple Music User Guide for Mac – Apple Support

Music Support Website:

Music — Official Apple Support

All the best :-)

Could you perhaps post a screenshot of what you see? Note you cannot add songs directly to smart playlists or playlist folders. Apple Music cloud playlists won't accept tracks that aren't in your iCloud Music Library, e.g. that have a cloud status of ineligible, error, duplicate, etc. See If songs are missing from your music library after you turn on Sync Library - Apple Support for details of how to view the cloud status of the tracks in your library.

tt2