I hope this is an appropriate place to ask.
I'm wondering if we can use a "fandom setting" if it fits the prompt? I have no specific plans at the moment but I do keep wanting to do some fanfic stuff.
actual rules clarification
Someone else asked me this in PMs so it's actually really good timing that you asked here, as I wanted to clarify it in-thread where it's visible.
My ruling on this is that a fictional setting or fandom for your story, I.E. the short story you write based on the prompt you are randomly assigned, is absolutely fine. The rationale behind banning them for prompts is entirely based on the fact that it could make prompts inaccessible for someone unfamiliar with a given setting. By contrast, if it's just someone writing their short story entry, then by definition whatever helps them write it it is all to the good. Beyond respecting site rules, we have no desire to meddle.
Now that being said, I think that you are quite right to say that any fandom you bring in should ideally flow organically from the prompt and not feel shoehorned in. That's not a rules question, because there's no way to legibly adjudicate that, it's more of a good writing question? There's a world of difference between getting the prompt "You are cursed into becoming a living snowman and have only 24 hours to break your curse or melt." and deciding to cross it with
Teenage Mutant Ninja Turtles, versus something like "You are a scientist cursed by their own invention, but for one day on Christmas you revisit memories of home and happier times." and making it about Bruce Banner, Victor Frankenstein, or so on. If that makes any sense?
Even then, I think it may be something of a high risk strategy, and it may be better to go with fictional conceits from media but with the serial numbers filed off, so to speak. For example you can easily write a story about Superman, and have people realise it's about Superman, without necessarily explicitly putting Superman in your story. The advantage there is that it can help the story to feel like more of a pure exploration of those ideas and themes, rather than like, being so bogged down in the specific lore and established characters of a given setting. Especially when you have only a short story to work with, this can be an advantage.
But everything other than the first paragraph here are essentially just my personal Hot Takes about how you might use other fictional settings in your stories. (This will to some degree be reflected in the judging but there will be at least two other people on the panel.) There a lot of SVers here who've submitted some great prompts, including some really experienced authors, so you might want to ask the opinions of other participants and start a discussion.
EDIT: I've stuck the actual rules bit in an info box just to make it clearer what is my personal writing advice, versus what is actually contest rules.