I used to be able to see my friends’ birthdays on one of the side panels on the Facebook homepage, but now it's gone and I can't find a setting to bring it back. Is there such a setting? And if yes, where can I find it?
It could not "be gone".
If you don't see your friends' birthdays on the right side panel on the Facebook homepage, it just means that none of your friends have their birthday today.
To see your friends birthdays, just consult the calendar.