I cannot see how to do this today.
Maybe, if I'm missing something, you might tell me.
It would be a very useful feature I think.

The Now Playing Tab is only for Inserting and Playing lists
You can not Save from the Now Playing Tab.

The Playlist Tab is for creating and editing playlists, you can save from the playlist tab.

There is a way to One by One,
***** a Card from the Now Playing Tab, to the Playlist Tab.

***** the Card, and hover the Center of the mouse pointer, on the Center of the Playlist tab.
If you are in the correct spot, the Playlist Tab will open, and you can then Drop the card
in the Playlist.

Switch back to the Now Playing Tab, and you can repeat the process for another card,