Is my fudge frosting supposed to stay this soft after a night in the fridge?

Freezing it and stirring is exactly the right move here, and no, it won't seize on you. Seizing happens when liquid hits melted chocolate the wrong way, not when you cool and stir an already-emulsified frosting. What you have is basially a ganache style fudge frosting, and those firm up as the butter and chocolate recrystallize. Your warm 78 degree kitchen is very likely part of the problem, butter at that room temp barely sets, so it looked glossy and thick while mixing but never actually got solid structure. The overnight fridge should have helped some, but if it's still pudding-soft after that, the ratio is probably a little heavy on the cream side too, which nobody can fix by waiting longer.

So here's my plan for you. Put the bowl in the freezer and stir it every 10 or 12 minutes. You're looking for the texture of thick peanut butter or scoopable fudge, where a spoon dragged through leaves a clean trench that holds its shape. That could take 30 to 45 minutes depending on your freezer, so check often because the center goes from perfect to brick fast. Once it hits that stage, pull it out and give it a quick whip. This is the part where it gets fluffy, and the reason yours never looked whipped before is that it was never cold enough to hold air. For piping specifically, err on the firmer side. Somewhere between scoopable and just barely soft is your window. If the swirls slump again, back into the freezer for 5 minutes and retry. You can also beat in a couple handfuls of extra chopped chocolate melted and cooled to lukewarm, which stiffens it up without changing the flavor much.

Rewarming gently also works, honestly. A short burst in the microwave or over a pot of barely simmering water until it's just fluid, stir smooth, then chill it properly this time, will re-homogenize everything and can actually rescue a slightly broken batch. Just don't let it get hot, or the butter separates out. And keep the cake itself in the fridge until close to serving tomorrow. At 78 degrees even a perfectly set fudge frosting softens fast on the counter.

Been there with a fudge frosting that went soupy on me mid-decorate. One thing that saved my sanity: stick the piping bag itself in the fridge between batches. Your hands warm the bag up fast and by swirl three everything's slumping again no matter how firm the bowl stuff is. I pipe a few, pop the bag back in the fridge for ten minutes, keep going. Annoying but it works. Also, how did the filling between the layers hold up? If that's a softer filling too, I'd frost the sides first while everything's cold, then do the top border last so it has the least time sitting out.

Honestly, even if the piping never gets stiff enough, you can always fall back on just spreading it. I did that once with a similar soft fudge frosting, scraped the sad little swirls off and smoothed the whole thing with an offset spatula, then pressed some chopped nuts around the sides to hide the texture. Looked intentional, nobody knew the difference. Also don't toss any leftovers if you end up with extra, that stuff freezes fine in a zip bag and it's basically instant topping for ice cream later.

I mostly do cookies so take this with a grain of salt, but one thing that's saved me on warm days is testing a single swirl on a piece of parchment and sticking it in the fridge for a few minutes before committing to the whole cake. If that test swirl holds, the rest will too.

Also kind of wondering, once you whip air into it, does it soften faster at serving time? I ask because my meringue buttercream turned soupy on a summer birthday once and I never figured out if the whipping was part of it or just the heat.

Update: chilled the frosting down and stirred it like suggested, and it actually firmed up into something pipeable. Did the single swirl test on parchment first and it held its shape. One thing I'm still unsure about though, the kitchen will be warm again tomorrow during the party. Should I keep the finished cake in the fridge and pull it out right before serving, or will a short time at room temp make the border slump again?