Maybe rip it out? The reason people use cedar is to prevent bugs and keep humidity down. With the wood now covered, there’s no reason to keep it. You can do another wall covering or paint.

You have basically ruined the closet, so I would just put a couple coats of paint on it and see if the wet smell goes away, or rip it out and sheetrock the closet.

Cedar contains resins that prevent many finishes from curing and staying cured properly, especially in a closed environment.