Wow. Why does a CG ship even need to be that huge...
The Japanese have two that are about as big, the Shikashima class, PLH31 and PLH32. The displace full load close to 10,000 tons. These Chinese vessels displace 12,000 tons.
They are good for very long distance patrols and escort duties and are large enough to provide significant humanitarian aid if necessary.
Specifically, the two Japanese vessels were built to to escort plutonium transport ships travelling from Europe to Japan, for patrol missions by the Yokohama Maritime Safety Department to sail to south-east Asia to fight against piracy in the Strait of Malacca. And, as stated, to make long distance patrols, show the flag, or conduct humanitarian efforts.
I imagine the Chinese have something similar in mind.