It does if you consider the part going to your county:
“In 2022, the federal government spent … This is 13.6% of the total spent on elementary and secondary education in 2022. The remaining funding comes from state and local governments, which contribute 43.7% and 42.7%, respectively.”
You've misread that. It is not saying that 43.7% of the state budget goes to elementary and secondary education. It is saying that 43.7% of the funding for education comes from the state. Those are completely different.
“In 2022, the federal government spent … This is 13.6% of the total spent on elementary and secondary education in 2022. The remaining funding comes from state and local governments, which contribute 43.7% and 42.7%, respectively.”