Export As is in fact 1st party UXP plugin. To my knowledge, it does not use Action Manager code under the hood but rather calls different PS internalls for image export. Therefore, it is not recorded. And for UXP plugin itself to be recorded, it needs explicitly made support for action recording.
I think people complained about that missing action, like about 10 years ago, when it was based on NodeJS and a generator plugin, I think. Is it still non-recordable today?