You can Tyvec the inside, insulate with fiberglass and cover it with drywall or anything else you want. Tyvec will let vapor pass through and you shouldn’t have a mold issue. Make sure you seal the seams of the tyvec to prevent air infiltration.
Cauk is going to come loose some time down the road. As long as the battens are reasonably tight I would just painter up.
There are otherways….got to run more later