ECO doesn't necessarily save battery/extend range ... it merely softens the acceleration and braking effects when you press the respective pedals. With fine control of your feet you can achieve the same range in Sport as you can in ECO.
For what it's worth - in my case (same car as you) at 100% charge, ECO + AC On might show 186 miles whereas Normal + AC On might show 176 miles on the GOM (Guess-O-Meter). So about 10 miles more.
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