Oh, it was "done" for me before that, but that's one of the stronger aspects of, "Really?" these characters, mostly Mariner, are too Meta. I think really it was "done" for me with Mariner's listing of "member berries" at the end of the first episode where she's name dropping a bunch of people/things she can teach Brad about as her protegee.
And the show runners have taken a stance that they're not making fun of Trek here but... At times it kind of feels like they are. Like Mariner's yawning fit at the start of the episode a couple of weeks ago, almost more feels like making fun of expository scenes setting up the premise of an episode. I mean, that's kind of making fun of things isn't it?
And the bad part is the expository information was interesting,the set-up of the "generation" ship was interesting, then we get Mariner yawning at it.
I also know it's a comedy, but it's too heavy sometimes, seems too mocking, and it's hard to make this "fit" in with everything else from TNG-era Trek. It does fit better that this is a "show within a show" and not actual events. But that doesn't quite work either because the internal references are just too obscure a show inside the universe would have in it.