I want to understand how swapping the box affects the item’s overall condition rating and scarcity value

disclosing the full truth might lower the resale price and make it harder to sell

Games are meant to be played, not hoarded like some financial asset. Play it and enjoy it, or make it look nice if you're putting it in a display. Fuck what other people might think, enjoy it for yourself!

I wonder if anyone here cares about resale value. This community is about gaming.

Unless the case is special like some of those jewel CD cases I'd just look for a aftermarket replacement you can transfer the box art to.

In general the condition of the contents is what's important. Case condition doesn't really effect resale value unless its very badly abused, in which case its very common to swap it out. If it's a special style case, like the original ps1 long boxes, if you have that style box, it doesn't really matter if you had to swap cases. If it's a generic jewel case, it matters very little. I think this is because the cases were generic and interchangeable from the factory, and prone to breaking anyway. If you want to be a stickler about it, maybe keep the original case with the package, but keep the game and acessories in something nicer.

Do they make replacement boxes? I regurally bin cracked jewel cases for games and music discs. Collectors don't care about the jewel cases unless there's something unique or special about them. Just swap the case if possible.

Over $100 I'd get a refund

Under I would look for a replacement box

Not advice on what to do exactly, but why do you say "long box"? I know many PAL and NTSC-U Saturn games came in special, long boxes, but I can't recall ever seeing a Japanese Saturn game in anything other than quite standard CD jewel cases (special edition carboard outer boxes aside). Particularly Kaze no Regret, which is a fairly common game here (a regular jewel case copy still usually goes for under 1,000 yen, even with obi and other ephemera).

If you want to, it should be possible to pop the broken cover out of the hinge piece and replace it with the cover from almost any standard double-width CD jewel case. There are several videos on YouTube showing how to do this. Once you put in the paper insert, no-one would ever be able to tell.

I don't have a ton of physical media, definitely nothing rare or valuable to anyone but me, but what I do own I care more about the condition of the media itself and associated artwork than I do about its packaging. From the pics you posted it looks like the plastic wrap is the resealable kind, I'd just swap the box out with a different one and put it back in the plastic wrap.