EndNote uses straight quotes ’ and ", but many users prefer smart quotes, ‘, ’, “ and ”.
I have struggled with this for years, and I recently found a work-around that exploits EndNote’s ability to handle characters in many different alphabets. After importing a reference that includes single or double quotes into EndNote (I use V 25.2), one can overwrite/convert the straight quotes to smart quotes as follows (on a Mac): option+] yields ‘, option+shift+] yields ’, option+[ yields “ and option+shift+[ yields ”.
In Windows, I understand you will need a physical numeric keypad with Num Lock set. The keystroke combinations should be, in the order used above: Alt+0145, Alt+0146, Alt+0147 and Alt+0148.