Archivist of Oghma — ruling 1

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.

Archivist of Oghma — ruling 2

Archivist of Oghma's triggered ability won't trigger if you search an opponent's library or an opponent searches another player's library.

Archivist of Oghma : règles, fonctionnement et interactions (MTG)

Archivist of Oghma is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Flash Whenever an opponent searches their library, you gain 1 life and draw a card.

How it works : Archivist of Oghma

Original English text — Wizards of the Coast / Scryfall

#1June 10, 2022· Wizards of the Coast
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.
No other card is named in this ruling.
#2June 10, 2022· Wizards of the Coast
Archivist of Oghma's triggered ability won't trigger if you search an opponent's library or an opponent searches another player's library.
No other card is named in this ruling.