I agree that the biggest problem of China is the local governments debt,not Evergrande.
However,I think that the central government of China and the PBOC have enough reserves to support the local governments to pay their debts,at least for a while.The reserves aren't that big,the huge crisis with come,when China runs out of it's foreign currency reserves.AFAIK,China owns lots of US government bonds.
They could sell the US bonds and get some cash in order to pay off the debts of the provinces.
The economic growth of China seems like a bubble that will pop some day.I'm sure that the new Great Depression will begin from China,not from the USA.