Possible Code Issue?

The Uno does not have an I2C address when you run your sketch but if the scanner found a device a 0x40 then it is almost certainly the PCA9685

Your problem is almost certainly power related. Power the servos from your external supply using the screw connectors and power the PCA9685 from 5V and GND on the Uno. That is what I did and it works

As a matter of interest, are any LEDs of the PCA turned on when you power it as you describe ?