Carpets placed on llamas don't update the look of the llama.

Happens with wandering trader llamas, wild tamed llamas, and bred llamas. Happens with first time placing or replacing carpet.

I have found a mitigation which is to leave the area or cross dimensions and come back, and then it will be updated.

Switch, 1.18.30, local single player, Simulation 4, Render 12, Survival