Spongy green figs
Our fig tree which is over 30 years old has been potted in 20" dia. pot 20" high; the tree is 10 feet high, spread across 6 foot, trunk midway 3.5 inches. Up to 28th July 2017 we already had 60 figs with still over 50 ripe figs on the tree. The tree was blown over on the 28th July and had broken the root in to ground from pot. I was surprised to find the heavy root in the ground. We stabilized the pot and watered regularly to compensate for the lack of ground root, the tree was pruned in the dormant period. It is now 29th June 2018 and I thought the tree had recovered, it has about 60 green figs but when I feel them they seem to be spongy the leaves are drooping. Over the last week the weather has been hot. So I thought it would be good lightly water every day, have I over watered the tree and will it recover or is there another reason for the spongy feeling? I am not a gardener, can anything be done to save our much loved fig tree.
From your description it appears to be a problem from water deficit, not overwatering. The tree was dependent on the root in the ground and when that broke off the reduced root system remaining in the pot kept it alive.
Now with increased heat, drought pressure and demand for water the minimal root system is not enough to supply water and nutrients. That's why the leaves are wilting and why I believe that the fruit is not turgid.
Step up the watering to a full flooding and soaking of the soil in the pot.