My issue is that you said they're capitalist. They're not. They do use a market economy in addition to a planned economy, as part of the overall socialist economic system. It's not a binary either-or; using a market economy doesn't mean it's capitalism, and planned economy (intervention) doesn't mean it's socialism. When I said they're structural terms, and relate to purpose: capitalism's purpose is to maximally extract profit and concentrate wealth; socialism's purpose is to better the lives (materially and culturally) of its people. China, as a socialist system, takes advantage of the benefits that a market economy can offer (efficiency, competition, resource allocation, demand and pricing signals) but doesn't use it to extract and concentrate wealth: instead, it uses the net benefits of the market economy to benefit the people. Similarly, a purely planned economy can be very stable and fair but is prone to stagnation and slow progress. By using both systems simultaneously, taking the relative advantages of each, China is able to benefit from efficiency and stability. There's also no pure free market economy: every capitalist economy has degrees of government intervention (another name for planned economy), especially in times of crises.

I also don't know what you meant about a "strong central government" not making them communist. That seems like a strawman. Nobody would say that a strong central government makes it communist, or a lack of a strong central government means it's not communist. "Strong" with no other qualifies is also not very useful: do you mean tough and resilient, or do you mean controlling?

I weighed calling them socialist, but it seemed… unhelpful when what i was trying to highlight that the unemployed youth are relying on family, and not the state.

This is a trap that people keep falling in to. Just because a socialist country doesn't do "good thing X" doesn't mean it's not socialist. No system is perfect; the difference is that the CPC makes strong plans, sticks to them, and publishes progress reports to address the problems that do arise. Should the state be taking the burden here where family currently is? Perhaps. But it's failure to do so doesn't mean the system isn't socialist. Again, I'll repeat my earlier statement: being "socialist" is a statement that is about the purpose of the government and the relation of the government to its people; it is socialist if it is for the benefit of the people en masse. Being "socialist" is not a statement of a utopic ideal antithesis to capitalism.

If you truly are willing to read about this, the book I mentioned is a good overview of China as it exists, as an implementation of a socialist society, at a level that does not require previous knowledge of theory or of China. Being intended for a foreign audience, it makes a concerted effort to address common misconceptions held by those outside of China about China. It's also very heavily sourced: each chapter ends with several pages of citations used in that chapter, including primary sources from CPC members, official government documents, analysis and critiques, and "historical"/foundational texts.

Highly recommend this book to understand how China actually works https://redletterspp.com/products/the-east-is-still-red