You should probably have an error in your errorlog about having two of the same material defined WOOD, step 1 is cleaning that up.
Now since farmable plants are harvested as a PLANT item (rather than when a natural tree is cut produces a WOOD object ie a LOG) so there are a few ways of doing this.
Both of which require REACTIONs to get the WOOD from your PLANT.
The reaction can straight up take a [A:1:PLANT:NONE:PLANT_MAT:MUSHROOM_WOOD:STRUCTURAL]
creating the product
[PRODUCT:100:1:WOOD:NONE:PLANT_MAT:MUSHROOM_WOOD:WOOD]
[PRODUCT:100:1:SEEDS:NONE:PLANT_MAT:MUSHROOM_WOOD:SEED]
and that would be that, but due to (I think it still exists) custom reactions have bug were a stack of 5 of these mushrooms would yield 1 log same if a solo stack was used (I think I had this conversation with another Reaction modder and I may be wrong and it will do a 1:1 ratio just fine) but I know the safest and best way is to use MATERIAL_REACTION_PRODUCT on the STRUCTURAL material defined
[MATERIAL_REACTION_PRODUCT:WOOD_MAT:LOCAL_PLANT_MAT:WOOD]
and
[MATERIAL_REACTION_PRODUCT:SEED_MAT:LOCAL_PLANT_MAT:SEED]
Rest is just following how vanilla tanning works, if you need more help I'm happy to keep going