No, sorry. FWIW, we generally very much recommend to use the Save to Zotero button in your browser to import items over relying on PDF recognition. While Zotero does aim to do as well as possible for PDFs, browser import is almost always better.

If you have access to the PDF on the page to manually download, Zotero will generally be able to grab it automatically. If that's not happening, can you share some specific URLs?

I would very much like this function as well. Sometimes I get articles or yet-unpublished pre-prints send by email from colleagues. It would be very convenient to be able to save them in a dedicated folder, which Zotero monitors and automatically imports all PDFs in that folder. Other tools, such as Mendeley and even Endnote now have this functionality.

I also often have some local pdfs so I would really appreciate this feature

I meant the pdfs that can't be downloaded through Zotero Connector. I often Print out Browser Protected Pages, or scrolling screenshot other software UI