Thank you all for your responses.
I will not clip his flight feathers once they have grown back in. How many molts does it usually require and how long do you think it will take?
The woman who found him did try to find the owner (she tried some local vets and online social media). No luck.
His cage is 17" x 17" x 24" high. I did add more perches after he initially fell, and put them closer together. He's now getting around the cage without issue.