First you will find the pickaxe here in this room but you will need to find the key first which is inside the rooms on top of this one
I encountered the same bug as you. I used the costume from Patreon, which has a buff that can increase the collection items. Now my story backpack is full and I can't discard the items in it, so I can't see the key to get the pickaxe, and I can't pick up the planks. They won't ask me to pick up 200 small wood sticks, right?