In theory what you want to do sounds simple.
Yes, a light sensitive diode aimed straight at the screen might work. It would probably obscure the screen a little bit.
You can also use a small microcontroller, like an ATTiny85, to read the light sensor, and control a servo.
You can use a "micro" size "park flyer" servo to make it somewhat small, although it'll be bulkier than a phone still.
Then you need some way to power the thing. I think that will be the hardest part. A single LiFePO4 cell or LiPo cell could do it.
In practice, trying to tie a servo and some circuitry to a phone that you keep in your pocket or bag or whatever... unlikely to be robust :-)