Correct wiring of a ADS1115
I'm concerned that I've connected the unused A1, A2, A3 to ground


I'm concerned why you shorted the Pot to the ground ( along with A0).
When the wiper goes to V+, you will be shorting the LED between V+ and 0V without a current limiting R in series. Confirm cathode (-) on LED is on correct polarity.
you will get slightly better signal quality for &gt;  ~10cm wires using a twisted gnd. around signals. This gives some protection from stray pulse noise.  1k pullups improve even more for I2C.

+1 for neat layout/  -1 for no schematic {even on a paper napkin;}
let's see if YOU can follow my layout edits without a schematic