Blood Operative

• WOTC Official Reminder Textofficial rules
  Lifelink — Damage dealt by this creature also causes you to gain that much life.

• WWizards of the Coast2018-10-05
  Official Ruling
  If you surveil and put Blood Operative into your graveyard as you do so, its ability triggers once you've finished surveilling.
• WWizards of the Coast2018-10-05
  Official Ruling
  No player may take actions between the time you choose to pay 3 life and the time you return Blood Operative to your hand.
• WWizards of the Coast2024-01-12
  Official Ruling
  An ability that triggers "whenever you surveil" triggers after you're done surveilling, even if you have fewer cards in your library than the number of cards you're instructed to surveil. It even triggers if you have no cards in your library.

Rulings via Scryfall