Isn't the CCP given explicit power and privilege in the Chinese government
The CPC (not CCP) is the guiding force of the government, and adapts to the will of the people through the mass line/being comprised of 10% of eligible persons. The highest level of the CPC (after the various levels of party committees/congresses) is the SC of the Politburo of the Central Committee, which is comprised of members elected through all levels and with terms of five years, and the highest individual position is the General Secretary (also terms of five years), elected by the Central Committee. Provided the persons in these positions are fit to serve, there are no definite term limits (one can be elected for a term of five years indefinitely until they are too old to serve (age limit), wish not to in which case a subordinate would the replace them, or are voted out by the CC) although I fail to see how a term limit can be justified when it is merely an undemocratic method of preventing the election of someone regardless of their success/the will of the population.
Xi Jinping was re-elected as GenSec in 2022 (third term), so the Central Committee would foreseeably be doing a new election in 2027 (for the SC of the Poliburo as well).