“Did anyone remember to buy a healers kit?”
There are some situations where characters would behave smarter than their players. That’s why we have passive checks and other checks to see if the character thinks (or even remembers) something the player doesn’t.
One of those situations is remember to leave the house with their winter coat when in the middle of the darkest months. It’d be cruel for a DM to suggest that since the player didn’t specifically say, “I’m going to dress up warm,” that the character would be wandering around in a t-shirt and shorts.
Similarly, when you are on floor four of a mine, where the job was to collect a few diamonds, only to realise that no one noted down a pickaxe, the group should be given the benefit of the doubt. Obviously the character would have considered this and picked one up.
Full disclosure: I’ve not actually read Blades in the Dark, and only know it from the Adventure Zone, but it has a nice system for this kind of thing. Before setting off on an adventure, the players decide what loadout they’d like to take. I believe these are along the lines of light and heavy.
The items in those loadouts aren’t decided immediately, but are decided in the adventure as they’re needed. If you’re going in light you can get away with a small handgun or an iron file or some such. Small things. Too many small things will eventually add up to a heavy load, so at some point you can no longer add more things.
A heavy load means you can start pulling out great axes and whatnot. The downside here is that (even before you’ve decided on what items there are) people around you will know you’re packing. Suspicions are going to be raised pretty quickly.
These loadouts might cost an upfront payment, but making the group pay for the items at the end might be more fun, adding a push-your-luck mechanic. Shall we splash out on a Scroll of Detect Lies now? What if it reveals nothing? What if the dungeon is a bust and the PCs end up going into debt? Drama! Tension! Oooh!
The DM can of course have final ruling on what a loadout contains. Maybe it doesn’t make sense for the PC to be carrying a glass making kit. It’s important to remember rule one of being a good DM though: at the end of the day, your job is to make the players feel like their characters are heroes. If that means they pull the perfect macguffin out their ass and it makes for a cool scene, then why on earth not.