At its core, the goal of the two regimes (China, Nazi Germany) is the same: control information so that the existing regime is portrayed in a good light that preserves stability. Just because China isn't genocoding Jews doesn't mean they don't have hundreds of thousands of political prisoners, disadvantaged minorities, and a completely authoritarian government. As is, you would never hear of the North Korean concentration camps that China supports, nor the Tibetan and Uighur genocides that are ongoing.

Google's move is purely financial. Google's biggest ambition is to control Chinese search, but its greatest ambition is to control all search, and the internet as whole. Google, as all other appreciably large tech companies, wants to hold a dominant position in the Chinse market, and to do so is willing to sacrifice market share in inferuor products. How much China gets involved is TB.

The really fun part? Watching corporate entities justify genocide, sexism, racism, etc. in their grabs for dominance over the remaining European provinces.