An adding-to-library shortcut for a paper I'm looking at

Is there such a thing?

Welcome @Oren to the Paperpile community! You can add papers to your library from your browser toolbar using the extension, which can import paper metadata and PDFs (if available) from hundreds of supported publishers’ sites. A green arrow appears on the P button when you’re viewing a supported site. Click on the button in your browser and then click the Add to Paperpile button:

The paper will instantly available in your Paperpile library, where you can cite it in manuscripts, read the PDF using the PDF viewer, share it with collaborators, etc.