What normally happens when you stare at an Enderman in survival, it will come towards you and will also occaisonally teleport if you stared at him further away.
However in 1.16 and 1.16.1, they kind of became broken and don't really teleport anymore.
I am unable to reproduce this issue in 21w19a. Endermen seemed to teleport normally as they should and their behaviour didn't seem out of the ordinary at any point.