I appreciate all the advice! I still have to dig up the exterior but there is no growth of any kind on the interior side of the beam. It’s drying out and getting less soft as it dries, but still soft enough that I can stick needles in it ~2cm. The bottom side is the softest. I used a syringe to squirt in some wood hardener.

I am tempted to use pro-grade hydro PVA and plasticizer in the exterior concrete then finish with a waterproofing clearcoat that claims to still allow breathing. I believe that will mitigate rain saturating the facade. But on the inside wall I am tempted to not even plaster and just leave the brick and wood exposed. I would then expect water to not penetrate from the outside, but if it does so anyway then at least it could breath on the inside. I can also monitor it that way.