Rust is the same chemical reaction as fire, oxidation.
It also releases the same amount of heat as a fire, except it takes a lot longer so save the marshmallows, lol
The reason paint or a sealer prevents rust is because it keeps the oxygen away from the metal surface, but if you paint over rust you won't stop the "fire" just slow it down.
Water speeds up the rusting because it is a fluid and H2O, the fluid allows more movement of the chemical reaction, like stirring a fire makes it bigger, and the O in H2 O is more oxygen.
Salts increase the reaction as well.
So dry and painted/sealed is the way to prevent rust.
Inside the door will get moisture from rain and condensation, so an open drain at the bottom and reasonable venting is required.
But as said above sealing the surfaces inside of the door is a good idea, but you need to neutralize any rust that has started first.
Naval Jelly can neutralize rust but will also remove paint, and irritate skin and lungs.
Use the Naval jelly and then rinse the surfaces with water, make sure it is completely dry, i.e. wait a day or two, then cover drain and apply a sealer or primer, something the will stick to metal, then remove drain cover.