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Hi! So @silverlinedeyes has extensively covered this in her lightsinger theory post and the follow up to it but I believe that the explanation for Azriel’s reaction (as a whole) is that he had been inadvertently lured in response to Gwyn’s potential powers.

The passage right above what you sent discusses how a “faint, beautiful singing followed him” down the stairwell after his conversation with Gwyn with Azriel swearing that his shadows “sang in answer” (which parallels Nesta’s powers reacting to Gwyn). Azriel then he “found himself” at the library when the clock chimed seven, against his intention to go to the market square.

The passive language - everything is happening to Azriel as opposed to him consciously making these choices, the “glowing image,” and the faint singing that followed him points to some magic at play. His faint smile could be him somewhat happy at the thought of somebody appreciating the gift he bought for Elain or it could be part of whatever lure Gwyn inadvertently (or purposefully hahaha) used on Azriel.

Regardless, the bonus chapter is inconsequential as it really just confirms what ACOSF seemed to hint at extensively - Elain and Azriel’s budding romance, Gwyn having certain powers, tension between the different courts and the possibility of war, etc.