Add carved wood mob heads like the chiseled sandstone creeper face.

Each wood type when carved (chiseled) would take the shape of the head of a passive or neutral animal mob native to a biome where that mob is common. Some examples:

Birch: Pig

Oak: Sheep

Spruce: Wolf or Fox

Jungle: Parrot or Panda

Dark Oak: Cow

Acacia: Llama or Ocelot

If you want to include more mobs you could give stripped logs a different build path to chiseled heads. It would make sense for the stripped logs to lead to the heads of smaller mobs such as chickens, bees, and rabbits.

Or just make a menu of choices you could make while working with wood at a fletcher's table (which you could rename carpentry table without changing how fletchers do their thing).

Other Ideas:

* Sculpted ice blocks could represent dolphins, squids, axolotls, etc. Blue ice as glow squid would probably be best.

* The stems of nether fungi could be cut into piglins (crimson) or zombie (warped) piglins.