I have seen every episode of The Muppet Show multiple times, although some of them not recently. Watching as a child, I (foolishly) tended to worry about the continuity of Pigs in Space. For example, in one episode the crew and indeed the whole ship were turned into food. Doctor Strangepork's head turned into a bunch of scallions, and the crew began eating the Swinetrek. Yet by the next episode, the whole problem had gone away as if it had never been. This concerned me.
Another thing that concerned me was why the pigs were flying around space and what their mission actually was. So far as I can recall, that was never answered, or even much alluded to. Piggy at one point does disclose that she was extensive trained for the mission (and, by implication, Link was not), but that's about the closest I think it ever came. As a subscriber to Muppet Magazine for the first several years of its existence, I recall several Pigs in Space articles in the magazine, but again they never explained what was ultimately going on.
So I don't think there is an "in-universe in-universe" answer. (The straight in-universe answer is that the Pigs in Space are performers in a third-rate comedy/variety show.*)
*Kermit [under his breath]: Second-rate comedy/variety show.