Let's say China does invade, overwhelms Taiwan's military, holds the island, or most of it.

Then what? Coalition forces bomb Taiwan - try to retake it?

Or do they bomb targets in China, as well?

Both parties would likely prefer to keep it contained - along the lines of the Ukraine War - so bombing China is a big step - invites retaliation. That's your WW3 scenario.

Though even if it's limited to Taiwan, the economic fallout would be colossal. Controlling chip production alone would be crippling.

That might be the war game CCP plays - prep-up with steel, essentials, launch a contained war on Taiwan (that doesn't damage the chip factories) - sink everyone else by shutting down the supply chain. See who blinks first.