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If you meant a prerecorded voiceover seemingly reacting to things in real time, that's The Tape Knew You Would Say That. It covers actions too, so it's also "The Tape Knew You Would Do That".
I'm otherwise not clear on what "an obviously post-recorded voiceover responds to action on-screen as though it were being recorded on site" means. Are they just a Narrator? They might be a Lemony Narrator if they're being particularly weird about it.
Edited by KD
It's where The Narrator (on a cooking show or let's play, respectively, in the examples) is recorded after the on-screen action, but reacts to the on-screen action as though the narrator was there - reacting to jumpscares, vocalizing in response to the in-game avatar taking damage, etc.
There's a thing I've seen often on Binging with Babish and The Backlogs among others, where an obviously post-recorded voiceover responds to action on-screen as though it were being recorded on site - saying "Whoop" when dropping an ingredient, or offering a "Glurk" when an in-game avatar is smashed by an enemy's hammer. Is this a Thing?
Edited by hobbitguy1420