If I accept a taxable grant that makes my income quite a bit higher, will it affect my marketplace insurance cost?

Yes, it will affect your Advanced Premium Tax Credit that is used to offset the cost of the premiums in the marketplace. 

Even though I will be spending it all on my business?  I have until Sept 2023 to spend it.  I can't afford to lose my health insurance, so I won't accept a grant if that is going to happen.

What you do with the money is irrelevant. The point is that is in income in the year you receive it. Any increase in income can affect your marketplace insurance.