” Firing missiles over Japan is a form of shakedown.”
True, but that is North Korea’s motivation.
For China I’d think they might still be concerned/angry with Japan and not anxious to push the Japanese to further rearm (or heaven forbid actually assemble some of there nuclear weapons).
Also, if China were to see a US action as inevitable then they are faced with an unwelcome set of alternatives: 1) Oppose the US militarily, 2) Drop support for NK, 3) Pressure NK into behaving. Avoid #1, Implement #2 early to maintain credibility, Pursue #3 (what’s to lose?).
China doesn’t want a unified Korea under the current South Korean government. It intervened in the Korean War to ensure that there would not be a pro-American government on its border. But they might prefer a more run-of-the-mill Communist regime there instead of the over-the-top madhouse the Kim family has created. Just like the Vietnamese Communist government intervening in Cambodia to get rid of Pol Pot...they might want to substitute a North Korean government that was more like a carbon copy of their own regime for what is there now...but that might be too hard to pull off (especially if Putin sides with Kim).