Why would China fight India though?
China unlike America has no strict need to map paint in order to keep themselves relevant. They already acquired economical and industrial advantage without having to invade anyone. They didn't even need to finish the civil war either.
Looting India would require more than just rolling in, India's "wealth" is all in population, unlike Iraq or Syria that has wealth in oil. So China would need to do nation building to see any long term dividends.
In the current status quo, China can easily shield itself from sudden crazy Indian aggression because of natural chokepoints.
The way I see it, China will just continue the 2020s and 2030s by keeping pace in the arms race. They will keep Taiwan out of reach for America like how America kept West Germany out of reach for the USSR.
Local "small" wars such as Ukraine that don't directly involve China but saps at NATO strength are a big benefit for China. More such scenarios will happen, and each time it causes a depletion of NATO, as well as swing states leaving America.
China is not in a hurry to end the civil war. Nobody is dying right now, and as stated above, China's greatest advantage is that it has everything it needs on the mainland. They may as well wait until America experienced its Gorbachev moment first before ending the KMT.
China will lose WWIII if it fails to addresse the India situation.. They aren't threat by themselves but they can be used as mercenaries.. It's a country of servitude and live for to serve others hence they will also provide the hand to eventually undo you all tho they themselves don't pose threat but anyone who has ambitions to march into China could make use of them..
This is why China will eventually get defeated by the Americans not because the Americans are strong just smarter geo-politically and empire building.
You can't grow if you don't understand what blocks your path or what can or could be a threat against you
In the words of Malcolm X..