Nope. It's $52B total in cash and tax credits from the government.
The $250B is the total capital from CHIPS and private investment. The other ~$200B is coming from private sector investments.
This is why the Big Fund is so big - it's been tough to raise private capital in China after the 2015-16 market crash so governments (central, provincial, and local) have had to step in to provide capital.
And if we're honest, the truly successful Chinese companies at the global scale (BYD, ByteDance, Tencent, PDD/Temu, Shein) always took private capital, and as such were able to outcompete state funded alternatives.