Equipment room constantly "damp" - How to insulate properly?

Hello everyone, a few years ago I built a carport at our place that goes around the corner along the house, so we use the large area as an open carport for garbage bins, bicycles, garden furniture, etc. (but it is now supposed to be closed off at the front with a sliding gate) and the small area that basically goes around the corner we have separated as its own room, through which you enter the house, with a built-in sliding door to the outside that has a cat flap and a wooden panel as a sliding door to the carport, above we made the light strip rainproof with plexiglass.

Classically built from 12x12 cm wood, clad on the outside with facade profile, paneled on the inside with OSB boards, above about a 30 cm wide light strip which is open in the carport area, clad with light panels in the separated room, below about 10 cm open between the floor and bottom edge of the facade profile, roof made of drip-proof trapezoidal sheet profiles, sliding door made of wooden panel between room and carport open all around (serves more as a visual separation and so that the dog cannot run away), sliding door to the outside from the room is not airtight, so there are gaps all around, but rainproof, with built-in cat flap.

Now I have the following problem: in the separated small room it is constantly damp in wet weather, so the garden tools stored there are damp and everything feels “damp,” the concrete walkway slabs are then almost all dark damp. It is said that there is not enough ventilation, although it is open at the bottom where the air can pass through and the “room” was not built airtight.

Now I am considering sealing the room completely and insulating the roof and the wall, the sliding door to the outside will not work because it is an OSB panel with an outside facade profile and runs directly along the wall, plus the cat flap is inside there. But does that help or will the moisture accumulate even more because there is no proper ventilation anymore?

if you seal the hut and also insulate it, you also have to heat it. otherwise the thing will start to mold on you.

if it’s raining outside and wet, it can’t be dry in the shed either. the air is humid, it settles everywhere. that has little to do with ventilation. but as soon as it gets drier again, dry air comes in and dries the wood again. that is basically the principle of a carport.
osb boards are also a somewhat special case, as they already have a vapor barrier or something similar inside and thus moisture can no longer pass through. these parts tend to mold easily.

I am by far not an expert on this, but OSB does have - as payday wrote - a high adhesive content and therefore hardly lets water vapor through. Is that really a suitable material for cladding the inside walls of a carport? I would say as soon as there is moisture inside, it can only get out with difficulty.

Probably boards with tongue and groove are better suited for your project.