Paste to same website and paste to “new widget” area

I can’t seem to paste a copied element to a new page on the same website where I copied the element from. Is that not supported?

There’s also the issue that I can’t paste at all without creating a new container first. Would it be possible to paste to the “New widget” area (at the bottom of the page) when inside the Elementor editor?

The specific use case would be a template library for editors available from the frontend where they can copy container sections to use on the page they’re currently editing.