For multiple songs, you can control what publishing information appears on public or share links in the bulk editor.
To open the bulk editor, select multiple songs and click the Edit icon.
From here you can click the More options icon in the top right of the page and select the Show/hide pub info option. This will give you the control options to apply to all songs.
Hide publishing information
Writers list is not displayed on song page
Show writers, hide splits
Writers and publishers are displayed on song page, all split percentages are hidden
Show writers and splits
Writers, publishers, and writer split percentages are displayed on song page.