Starlit Soothsayer

• WOTC Official Reminder Textofficial rules
  Surveil — Look at the top N cards of your library. Put any number of them into your graveyard and the rest on top of your library in any order.

• WWizards of the Coast2024-07-26
  Official Ruling
  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.
• WWizards of the Coast2024-07-26
  Official Ruling
  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.

Rulings via Scryfall