If China really is a socialist country or one pushing towards communism, why do you think they are waiting to push more directly in that direction? What is to be strategically gained from capitalizing your economy, essentially going backwards for 50 years instead of continuing to push for communism?
This is not exactly the case. I don't want to speak too far out of turn since I'm not an expert, but one would definitely be misinformed to think that every (or possibly even a majority of) the CCP is a committed communist. Party dealings are more opaque than we are used to in the West, plus the language barrier, so it's hard to say much for certain unless you're really in the know. One thing that we probably agree on is that the Chinese political system is far more effective at actually getting things done (mostly good things at that) than the U.S. government, even if there are many liberals within it.
On climate: everything I've seen indicates that this is a major concern for the Chinese government, and they have begun to take measures to address environmental issues domestically, but it's going to be hard to do that all at once given that they are the world's factory at the moment. I would guess (pure speculation of course) that things will be looking pretty good on that front in 20-30 years, but there's a long path ahead.
When we talk about "climate catastrophe" it has less to do with the entire world ending and more that a lot of people are going to be displaced and or killed by the resulting effects. It's not China's responsibility to avert this alone, and it seems that they may be poised to lead the way whenever other countries are ready to actually address the issue. The idea of "pushing for a worldwide revolution" is incredibly dangerous and not really in the cards. Theyve been non-interventionist to a fault, and that's gotten them to where they are today. The American empire is decaying, but it's going to exist for quite a while longer. I think it would be a folly to depend on any one country to introduce/support some form of global socialism. More likely is that smaller developing countries develop organic symbiotic relationships with the PRC as the US declines into a middling level of relevancy, and form a socialist-oriented bloc over a very long time.