the white-gray stuff (fuzz or slime) should normally go away within a couple of weeks after introducing the wood in the water — some resources say they can last for months, too (never encountered that myself).
If you can, take out the wood and scrub the fuzz off thoroughly, otherwise do this in the tank with an old toothbrush.
Siamese Algae Eaters as well as otos would eat this, and shrimps should normally help, too (amano, specifically). If it still keeps coming back after months — this is beyond me.
When I said it is emersed, it meant that this is not under water (not submersed). I actually used a very young real tree I found in my mom’s garden, asparagus and some land moss. I am setting up a website for my kokedamas which also will be a webshop — I am not quite sure if these rock creations can be put on delivery, I think they would fall apart. But to do this you simply have to go to the nature, collect ingredients, and assemble it with some sticky soil, such as keto or what I used: swamp soil. Good luck, and if you do not mind, share your creation with me :)