The physical island is a huge geopolitical asset or security risk. See island chain strategy. Also look up elevation map of Taiwan + Taiwan straight. Chinese coast is very shallow and hard to hide Chinese subs, whereas east Taiwan drops straight into deep water which enables China to hide subs which is important in controlling regional waters against US Navy. Regardless, the Chinese military planning certainly doesn't pretend the land isn't there. The government (from both sides) just doesn't recognize each others sovereignty.

How do Taiwanese companies do business in China?

"Hello, I am the CEO of a company located in a fully autonomous province that does not pay taxes to the PRC?"

China does not occupy Taiwan, so those points are moot.

What security interest is served by censoring discussion of the existence of Taiwan?

This is a political issue, not a security issue.

It's both. Politics is a huge part, reunification is #1 CPC policy consideration since founding and her entire legitimacy rests on it. Occupation goal is by 2050. No one is censoring discussion of Taiwan? If you're talking flag emoji that's equivalent to banning confederate flag in Chinese context. People talk about Taiwan in China all the time but under context of reunification. On refusing sovereignty claims. If Taiwan was sovereign they would be free to host US bases which challenges Chinese security, particularly shipping lanes where China imports oil. China is not energy secure. Taiwan has been a Chinese "redline" for many reasons.

> If Taiwan was sovereign they would be free to host US bases

Taiwan is clearly sovereign, anyone saying otherwise is ignoring reality or avoiding offending China.

The US had military bases in Taiwan for 20 years, the military bases were removed to assist with normalizing relations with China.

I can absolutely see why insisting that the US not place military bases on Taiwan is a security concern, but this has nothing to do with the sovereignty of Taiwan. (Similar to US concerns about Russian military installationa in Cuba which were unrelated to Cuba's sovereignty.)

The institutional double-speak around the sovereignty of Taiwan is purely political and has no impact on actual security issues.

I like to compare it with the Cuban Missile Crisis. Imagine having that Soviet (in this case US) power projection so close to home.