I mean they are instantly targeting the moment they appear on the screen, no matter what direction they spawn relatively to their position and facing.

This is actually possible with the in-game auto-targeting setting. You just write a script to constantly spam 1, and then when an enemy spawns nearby, the auto-targeting function targets that enemy and instantly rotates your character to face it.

If the bots were written to check for nearby entities and attack them, then they would attack at invisible entities before they appear on screen, since all enemies are first spawned in as invisible objects. You can verify this by spamming an AoE on a spot where you know enemies will spawn, and watch yourself get put in combat before any enemies appear on screen. Sometimes you can kill them before they appear, and then just their corpses appear. Since bots are waiting until the enemies appear, they're using auto-targeting.