No, it started as an adorable meme on Chinese forums:

It then became a racist trope on Western forums.

The title of president is ceremonial, so term limits on it are hardly consequential. The real top position since 1982 has been the General Secretary of the CPC, which is a renewable five year term. Xi is still very popular with people in China, so it’s no surprise that he won a third term in 2022. Jiang Zemin also won three terms, so there’s nothing unusual about it.

And why wouldn’t Xi be popular?

• Most in China Call Their Nation A Democracy, Most in U.S. Say America Isn’t
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• Helping 800 Million People Escape Poverty Was Greatest Such Effort in History, Says [UN] Secretary-General, on Seventieth Anniversary of China’s Founding
• China’s Energy Use Per Person Surpasses Europe’s for First Time
• At 54, China’s average retirement age is too low
• China overtakes U.S. for healthy lifespan: WHO data