Chinese economy is not about catching up with the west anymore. If you ever lived in China in recent years, you'd see that the Chinese economy is advancing in lots of aspects, and many of those in ways vastly different from western societies. The government plays an important part in it, but private companies are just as important. For example, the tech industry in China (which comprised of mostly private companies) evolved into its own ecosystem, and is iterating faster than that of silicon valley.
All of these are good ideas, and China or South Korea is doing them. 1) Literal moonshot. Heard of Chang'e 4 which landed on 2019-01-03 yet? 2) Fiber optic. Ever wondered why South Korea is land of MMORPG? 3) Particle accelerator. Heard of CEPC yet? 4) Every student at university. Check South Korea.
China (and South Korea) is doing them and tens more. Yes, some of it will fail, it's natural. But there are lots of "the next thing to do", it's not "less obvious" than what came before.
You say that the USSR got close to the leading economies in the mid 60's. But that does not explain why they fell so far behind afterwards. How come they did not continue to be just behind for the succeeding decades?
It's not that they couldn't develop any new technology. They had, and still have centres of excellence and technology sectors they’re very good at, just not enough across the whole economy.
This is why Russia is still such a backwater. It has never developed it's own internal marketplace for ideas, innovation, entrepreneur-ism and technical evolution. The Resource Curse and attendant corruption and political rent seeking has hit them hard. I believe that China has largely avoided this mistake.
It's wildly inefficient, with those inefficiencies previously covered over by the former rapid rate of growth.
You can see that inefficiency coming to light now, as they over-invest into stagnant state owned enterprises in their credit markets and deprive the private market of capital. That despite most of the employment, innovation, and growth formerly coming from the private sector. The reason they're doing that, is to fake growth, the only place they can immediately force-allocate stimulus spending is in the giant stagnant state owned enterprises. Several years ago all of their economic metrics went hard south, despite their claims about growth everything was indicating a near recessionary environment, so they fired up big stimulus programs and inflated assets such as real-estate. That stimulus was overwhelmingly focused on things they didn't actually need and it has resulted in mediocre growth. They're facing the exact same situation again now.
Their productivity rate has collapsed since they shifted to that perma stimulus model seven years ago or so. Once your productivity implodes, you can only grow by shoving capital or labor at a problem. They have a contracting labor market, so their options there are now mostly exhausted. Which is why China now has to constantly run capital stimulus programs with big shots of capital or credit lending to the state enterprises. Their economy is no longer growing rapidly organically. Each subsequent round of this produces reduced returns, because the last thing China actually needs is to produce a lot more steel or concrete or buildings (they have extreme vacancy problems in their real-estate market), and those are the easy targets for juicing the economy in a command style from the top. It also resulted in loading up their local economies with enormous amounts of debt, as the local regions & munis are part of the stimulus shoveling process of moving capital into the state enterprises and real-estate.
In regard to China, I think that they (like the Soviet Union before them) were very good at playing catch-up, because command economies are very good at getting everybody on board to do the thing which everyone knows needs to be done. "Do this, or we will put you in prison or worse."
However, once you have (mostly) caught up, it becomes less obvious what the next thing to do is. Literal moonshot? Fiberoptic internet to every house in the nation? Particle accelerator that can hit energies never before reached? Every student gets a spot in a university?
Some of these might be good ideas, some might be boondoggles. It's hard to know, when you're nearing the front of the pack. The Soviet Union was great at playing catch-up until, sometime in the mid 60's, they were too close to the forefront to be able to clearly see what needed to be done next.
China's Communist Party is great at getting everyone to do what they have decided to do. I think it is going to be harder for them to figure out what an economy, of their size and relatively advanced state, should be doing next. If they guess wrong, it will be ugly.