Archivist of Oghma

• WOTC Official Reminder Textofficial rules
  Flash — You may cast this spell any time you could cast an instant.

• WWizards of the Coast2022-06-10
  Official Ruling
  Archivist of Oghma's triggered ability won't trigger if you search an opponent's library or an opponent searches another player's library.
• WWizards of the Coast2022-06-10
  Official Ruling
  Archivist of Oghma's triggered ability won't be put onto the stack until after the spell or ability causing the opponent to search their library finishes resolving. Notably, if that spell or ability causes any other abilities to trigger (for example, if the opponent searched for a card and put it onto the battlefield), those abilities and Archivist of Oghma's triggered ability will go on the stack at the same time. The active player puts all their abilities on the stack in any order, then each other player in turn order does the same. The last ability put onto the stack this way resolves first, and so on.

Rulings via Scryfall