I'd attribute the error to the effects designers, not the writers. It's not the first time the FX artists have failed to do their astronomy homework -- there was that episode where they portrayed an O-type star as orange instead of blue. And it's not the first time they've failed to represent what the writers clearly had in mind; in episode 9, when
Discovery was doing its series of hundreds of jumps to break the cloak of the Klingon flagship, the FX showed the flagship just sitting there in one place, which entirely defeats the purpose of being cloaked.
A hundred AU is within Sol System's scattered disk, home to an assortment of cometary objects and dwarf planets, and possibly the suspected
Planet Nine, although that would be several times farther out. The verbal description reminded me of the version of Starbase One in the DS9 novel
Time's Enemy, where it was an antique space station in Sol System's Oort cloud. It's conceivable that the writers may have been thinking of that, and there was a miscommunication with the FX team.