What's a potential bending style you haven't seen anyone think of yet
Earthbenders bending trees. Treebending.
They should be able to bend the silica embedded inside the tree's structure if they're skilled enough. It's a mineral compound found in various rock types, and gets absorbed through the roots of trees.
This explains why Toph couldn't bend the dry wood in the prison cell in [S3EP7 The Runaway] (besides not having considered it, perhaps the silica content was too low or disconnected from the ground source for her to sense earth contents like she did with metal).
And why Haru, Tyro and other earthbenders could bend coal in [S1EP6 Imprisoned] (which is essentially fossilized plant matter that has become mineral/rock-like).
It's likely easier with petrified wood though.
