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.
I do believe that we should not be considering China as a great power if they fail to keep growing with debt. I mean look at the situation they are in right now, it is obvious that they should be able to grow with the man power they have, and they still fail compared to places that have quarter the amount of people they have with so much more wealth. I believe CCP will eventually fail not because they are not good at finances, but because of human rights problems.
There are other smaller and poorer nations that keep on saying they are willing to work for cheaper and western nations started to listen to them as well which is looking like taking away jobs from China and moving to other smaller nations. This is the real reason why China is losing, because they grew big and everyone is hating how they are treating both their citizens and everyone else so they are looking for other nations.