Don't eat moldy shrooms (a proper supplier would have dried them first, IMO, but it's been a while, and they're all millenials now so who knows?).
Tough to say. Wait, you're a total n00b? Yeah, I wouldn't go deep water submersible salvage op before a first potential trip. Esp. with shrooms. You might have a trip, to the ER when you barf them up extra hard but are too loopy to tell your roommates to just let you die where you are (to be clear, I'm going on the "don't eat rotten things you bought from the granola wizard on the boardwalk" theory of hygiene, nothing specific to Aspergilllus shroommelt, and I doubt it would hurt you--worse than real shrooms anyway).
And you say mushy . . . and wet. That's just weird. Supermarket Agaricus bisporus, the most commerical-friendly mushrooms, still go quick, but they get slimy.
So really, unless you won some Elon Musk 'n Me go to Mars Forever, Not Taking Spore Prints, I'd find a new source, or be bold to ask for dry (if a supplier is legit, he'd HAVE to have dried stock unless he eats most of it himself), look up some storage ideas (dried will keep forever) and make sure they're not just Enoki left in the light so the tops turn brown. Don't blow a potentially sacred and truly life-altering experience getting high on ergot or who knows what.
[Just thought, one thing with fresh shrooms is that you can make spore prints or just clone. Psilocybe's seem to really like cow patties, which is tough in your kitchen. Look up Paul Stamets books for a good substrate, dice up your soggy shrooms, and plate a bunch, separate and covered, keep the least-moldy least fruit-fly plates and then follow Stamets cultivation conditions. Maybe they're OK. Now I miss psychedelics. Up for days on meth is trippy, not quite the same]