Conventional conflicts can escalate into nuclear ones but not when done right. The US is in Syria today because Russian conventional forces are too weak. Otherwise, they can safely muscle the US out under the correct reasoning that Russian forces are invited by Syria's government while American forces are invading Syria. With the clear geographical advantage, if Russian conventional forces were strong enough, they would implement quick power plays and shut the US out before there as even a chance to get into a conflict that might go nuclear. The US dared to strike a Chinese embassy in Yugoslavia because Chinese conventional forces weren't all over the place with modern weapons breathing down the necks of their American counterparts. The 1993 Yinhe Incident occurred because China's navy could not protect its merchant ships; a more powerful conventional navy could have sailed to the Yinhe and guided it right out of America's blockade threatening unequivocal reciprocation to any use of force to stop them. There is virtually no threat of nuclear escalation in these cases. This is why people invest in the conventional military. They're not all idiots wasting their money.
As to the specific percentage that should be invested in the military for China, I don't know and cannot begin to do any calculations with the information available to me. In general, the less you spend on the military, the faster you grow your economy and thus in the long run you will increase your ability to afford and maintain a large military. However, the threat of immediate challenge and inability to keep up with modern weapons rises. The higher the percentage spent, the lower this immediate threat is, but at the price of somewhat diminished ability to afford a larger military in the long run. I trust Beijing to find this balance.
No, what we see in Syria is the Russian military and the US military really trying to deconflict and stay out of each other's way.
The Russians can't outmuscle the US into leaving Syria, because that would require active Russian support/attacks directly against US troops, with predictable consequences in escalation.
And the US can't outmuscle the Russians into leaving Syria either, for the same reasons.
And neither side thinks Syria is worth sending large numbers of forces, in order to win decisively.
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And it's not about the level of military strength per se, but whether there is a tripwire force and the objectives worth it.
In the Yinhe example, a single Chinese Frigate could have faced down a much larger fleet.
That's because the Chinese Frigate would know that the only way the US Navy could board the Yinhe, is if the US Navy attacked and sank it.
And that the Chinese military could credibly threaten to sink a US frigate in the Western Pacific in response.
So if China did go ahead and sink a US frigate, the US could respond with a conventional war. It would probably go nuclear, but as long as China has sufficient nukes, Mutual Assured Destruction means everyone loses.
If China did go ahead and sink a US frigate, and the US declines to respond, then both sides would have lost a frigate. Both sides would still be the losers from such actions and from the outright hostility afterwards.
And if China declined to escalate by sinking a US frigate in response? A Chinese Frigate would have been sunk, nothing found on the Yinhe, and the US labelled as an evil imperialist hegemon for decades afterwards.
In all these scenarios, the US doesn't win, and it doesn't depend on China having a huge fleet.
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For the past 20+ years, Beijing did decide to keep military spending at roughly 2% of GDP, in order to focus on domestic economic development.
And today, that does mean China has the spare resources to build a large navy
