During Artemis II, NASA's crewed flight around the Moon, why do the astronauts narrate what they see out loud in real time?

Answer: So every remark can be tied later to the exact image and moment, even during the radio blackout behind the Moon

So every remark can be tied later to the exact image and moment, even during the radio blackout behind the Moon ✓ — Correct! For part of the flyby the Orion capsule passes behind the Moon and loses radio contact with Earth, so nothing can be sent live. Speaking the observations as they happen, with the cameras rolling, stamps each remark with its moment, so afterwards the crew's words, the photographs and the timeline can be matched exactly, including the stretch nobody on the ground could follow.

Because Orion's clocks drift when the capsule is near the Moon — Wrong. Spacecraft clocks do not wander because the Moon is nearby; timing on Orion is precise. The narration is about documenting what human eyes noticed and when, for later analysis, not about keeping time.

Because Orion cannot store video well enough to review later — Wrong. Orion can record and store mission data and video. The point of narrating is to bind human observations to the visual record, so that a remark like 'that crater looks fresh' can be placed on the exact frame it refers to.