The Bookmarks app content is unique to your whole dashboard. If you duplicate it on multiple tabs, it will still hold the same content.
One way to overcome that limitation is to use various ‘tags’ in the Bookmarks app and choose to display one specific tag on each tab, as shown in the following screenshot.
For privacy reasons, you also can not duplicate or add a Bookmarks app on your public page.
Instead, you can use the 'Link module' app or copy and paste your list of hyperlinks in a 'Webnote' or 'Html' app.