I wish I lived near you, Jay.
I love figs, especially right off the tree.
Your fig squares sound yummy.
It have been quite a while since I have seen a fig tree so I am not sure how I cooked with them.
I remember freezing them for later use.
The only thing I thing I fixed with them was cobbler because it is the easiest.
I had a recipe called Essie's Cobbler that I used for everything.
This might be the same recipe:
https://www.cooks.com/recipe/y60a86gl/essies-cobbler.html
I bet figs would be good with my Clafoutis recipe:
https://permies.com/t/101228/RECIPE-Simple-Clafoutis