A bench in an outbuilding is a compromise, and the thing it compromises most is steel. Plenty has been written here about oil, wax and wiping a tool before it goes away. All of that assumes the building itself is sound. When it is not, no amount of maintenance keeps ahead of it.
Two problems that look identical on a plane sole
Rust from condensation is general. It appears across the whole face of the metal, worst after a cold night, and it arrives on everything in the shop at once, including the vice and the bench dogs.
Rust from water getting in is local. One end of the bench, one wall, the bottom drawer of a cabinet. It is worse after rain rather than after a cold snap, and the untouched tools three feet away tell you which problem you have.
The second kind is not a storage mistake and it does not respond to a drawer liner. Something in the structure is letting water in, and once a wall or a floor void has been wet for a season, drying it out is specialist work with meters and air movers rather than a matter of leaving the door open through the summer. Readers with benches in flooded basements have been pointed towards firms doing water removal and drying in Columbus and similar outfits elsewhere, and the reason is narrow: they measure moisture inside the structure instead of judging by how a surface feels, which is the only way to know when a room is genuinely dry.
Read the building, not the tools
Walk the shop with a torch after a wet week. A dark fan shape spreading from the base of a wall means ground water. A stain running down from one point near the roof line means the covering or a flashing. White powdery deposit on the brick means water has been passing through and evaporating there for a long time.
Timber tells you most. Press a bradawl into the bottom of a stud or into the end grain of a joist near the floor. Sound wood resists. If it goes in like cork, that is rot, and rot needs sustained moisture rather than an occasional damp morning.
What is worth doing yourself
Clear the ground away from the outside wall so it sits lower than the floor inside. Put a gutter on an outbuilding that lacks one, because a bare eaves line dumps water straight against the wall it is supposed to protect. Seal a concrete floor so it stops passing moisture upward into everything standing on it.
Then insulate, because the condensation problem and the ingress problem are solved by different work and both have to be done.
Move the irreplaceable first
While any of this is outstanding, take the tools you would mind losing into the house. Infill planes, a good set of chisels, anything with an inlaid handle.
A sealed cabinet in a wet room only slows the water down, and the tools that deserve protection are usually the ones that will not survive the wait. The ordinary ones can take their chances on the rack while the building is put right.