Have you considered embedding the PDFs in a Canvas page rather than linking them to open in a new tab? You could set-up links within the page that would help with navigating to each file preview without needing them to open in a new tab. If your Canvas Admin supports it, you could also see if they would be willing to add a theme customization to allow for tabs or accordions that is supported and accessible on both desktop and mobile.
I would be cautious about trying to design a button that opens multiple links. This isn't commonly expected behavior when clicking a link/button. This is more common as a design for spam/malicious intent, which is why browsers may also make efforts to prevent multiples tabs from being opened by a single click. I know your intentions are good for what you described, but it could create unnecessary risk if users begin to think it is appropriate for websites to open multiple tabs from a single click.