If you haven’t gained or lost life during the turn when your end step begins, Starlit Soothsayer’s last ability won’t trigger at all. Gaining or losing life during your end step won’t cause the ability to trigger.

Starlit Soothsayer’s last ability cares whether you gained or lost life this turn, not how your life total changed. For example, if you gained 2 life and lost 2 life in the same turn, you still gained and lost life that turn, even though your life total is the same as it was at the start of the turn.