The characters in Blades have pretty identifiable specialties and their gear tends to line up with that specialty. Faced with an obstacle that leans directly into that specialty there usually won't even be a conversation - using gear is always better than stacking stress. If I were playing the spider in the example above and the group decided that climbing was the way to go I'd just check off the gear and describe unpacking it. As I mentioned above though, the conversation is always possible and it is a matter of experience, as it is in any game, to have that conversation whatever way best scaffolds table goals.
The particular case of quantum equipment in Blades is one that can veer sharply from solidly diegetic to very meta in feel depending on how the group is handling things. It's also not a feature that everyone will love or even like. Personally it doesn't bother me at all, but we all have our caveats and peccadillos at the table.