Thanks for your feedback, @DSR! Adding labels while reading a PDF in Paperpile’s PDF viewer has been requested by users before, so I’ve added your +1 to the topic on our internal feature tracker. In the thread you linked to, the ability to add labels in the extension popup while viewing PDFs on websites is now available:
Ah yes, that feature is great thanks, makes a big difference. To be able to do it within the paperpile PDF viewer would also be great as sometimes you only know what folder or tag you want to assign a paper when actually reading it.