A fair bit, actually. China's political system is basically a popularity system from bottom to top. At the lowest level, politicians only stay in power if their population is happy. This trickles up to the provincial level, where politicians again only stay in power if their population is happy. At a national level, the national leaders stay in power by building, essentially, large cabinets out of different provincial and regional leaders - thus, their entire position relies on keeping the provinces happy.

It's not the perfect system, but Chinese citizens can fairly easily impact local and even provincial policy and, by extension, influence national policy (recently, by repealing the COVID lockdowns with mass protests).

The CCP isn't an absolute monarchy or something. At the end of the day, it serves it's people. The power of the Chinese economy is in its industrial capacity, after all, not in its wealth: the needs of the people need to be addressed to keep the country stable.