Vault Key fragments in Borderlands 4 are tied to resistance operations, not random loot caves. The snippets below recap what Gearbox has publicly stated.
As you traverse Kairos, keep an eye out for Points of Interest that you can claim for the Crimson Resistance. Clearing enemies lets you convert safe houses into fast-travel nodes or relaunch Order comm balloons to scout and track Vault Key fragments.
Source: borderlands.2k.com/game-info ↗
Clearing hostile forces from points of interest allows the Crimson Resistance to secure safe houses, unlock fast travel spots, and reactivate Order comm balloons that assist in tracking Vault Key fragments.
Official description ↗Gearbox has not yet published fragment coordinates or puzzle solutions. Monitor the Borderlands 4 news feed and update notes—those will be the first places the developers document fragment requirements once live content rolls out.