I also had this problem. I was able to work around it by setting print.prefer_system_dialog to true in about:config

For my system, I narrowed this down to a problem where Firefox hangs when trying to talk with cups. The moment I stopped cups (sudo systemctl stop cups and sudo systemctl stop cups.socket), Firefox was freed from whatever deadlock it was in, and my print dialog and PDF downloads immediately came back. I ended up stopping cups, deleting /var/lib/cups and /var/spool/cups, and starting cups again, which fixed the problem for me. Maybe some state files that cups stores were corrupted or otherwise problematic?