Government backed "cryptocurrency"?
Well, China already has a currency... it's the Chinese fiat currency... both digital and physical. I guess what the government needs is to fully convert the fiat currency into digital coin or just use stablecoin backed by the its fiat currency. A coin that does not have the main features of cryptocurrency do not really deserve to be called a cryptocurrency,in my opinion
It wouldn't be possible at all. Because the main thing we need to consider is the features just like what you've said, and the Chinese government will not possible allow that to happen. In the first place they've already developed a blockchain based identity system, and with this, it is probably they could identify their people and with cryptocurrency, they can't, and this is contradicting that is why it seems to be really impossible for them to even transition their currency to crypto.