More specifically, how many tiles away do I have to be before I get bonus accuracy on my shotgun? Closest things I've found are this reddit thread and At what range do various weapons get range bonuses?. The latter is for XCOM 2. The reddit thread says,
Shotguns have about 50 aim bonus at 1 range, 0 bonus at 10 tiles, 29 penalty at 15 tiles.
But the UFOpaedia link is dead.