China massively saves on power projection. They don't care about the ability to wage war half the world over as long as they could be powerful enough in their neighborhood.
Furthermore they know that it is not realistic for them to build an army stronger than the US one so they don't try.
No it's likely because China has a palace army. An army that stands against regime change and can only project power in limited, and ranged constrained ways. Why would you want a strong military when they could overthrow you and your bodyguards & loyal police & paramilitaries and put in place a general as the head of state? There is a reason civil-military relations are important in the US. Russia is somewhat like this, and Iran is somewhat like this but with two armies the IRGC, and the regular military.
It's not just the raw amount spent, it's also what it gets spent on. The US military spends a lot more on personnel costs, for example. It also has bases and commitments all around the world which cost a lot to maintain. What's distinctive about China is not the size of its military budget, but how much of it is spent on building new things and closing that technological gap as opposed to just maintaining the capabilities that already exist. In short, the US is already a superpower. It spends a lot of money on being a superpower. China isn't in the same category yet, which means it can spend money on building that capacity rather than maintaining it.
China and the US ultimately have nothing to gain by fighting a full scale conventional war. There is very little they could do to directly harm one another (short of breaking out the ICBMs) and the cost of attempting to do so would be astronomical.
In a few decades, China will have a significantly larger economy than the US. It's unreasonable to believe that the US will always be able to outspend China in the militaty. The big advantage the US has is that it is allied with most of the developed world. US global power doesn't just come from having the largest military, but also not necessarily needing to use it because regional allies are rich countries that are capable of defending themselves. What has kept Taiwan from invasion isn't the threat of US intervention, it's the fact that invading Taiwan, even with overwhelming conventional superiority, would kind of suck real bad.
The problem with that is that the US stands to benefit from being a hegemon, look at the dollar being the world's reserve currency/government bonds. It means they can borrow, and spend more on their military, infrastructure, R&D, etc. They also have the language of business, science, and international politics which is another amazing US superpower benefit. And most crucially the US given its status as a near monopoly on smart people, dynamic creators, and innovative contributors of original research who want to immigrate and are willing to learn the language. Plus a few of the less dynamic immigrants whom I count myself being despite my college degree can eventually be smaller contributors, have children that are contributors, and or loyal citizens if they aren't one already.
There was one story where China tried to open its currency, and rich Chinese people immediately tried to get money out of the country. Another where Western volunteer military enthusiasts using satellites saw how poorly maintained Chinese submarines are. Given how boring submarines are, but how critical they are in anti-ship warfare it surprises me to no end how poorly that decision was made to prioritize the Air Force maintainers over something that can literally sink an aircraft carrier, and sneak away the easiest.