I don't think supply and demand have to be seperate from LToV. Supply is the quantity and quality of a commodity, while demand is the want or need of a commodity. Demand is self-explanatory. If you elaborate further on supply, the way you increase supply is through extra labor, either making more commodities or by allocating more time to their production.

Marx and Engles were directly refuting Adam Smith who couldn't come up with an explanation for why prices didn't change when supply or demand changed, even at macro scales. Smith thought this discrepancy occurred due to "the invisible hand of the free market." He was being literal, as in God was the one causing or not causing these changes. Marx and Engles came up with the real answer based on work by Ricardo: the discrepancy was due to profit. When prices change, it's the capitalist economy having profit realign with value that's been stolen from workers.

I want to leave it open. Someone might argue that the labor cost is itself determined by supply and demand, for example.

*Basically, I don't know what lines of argument I should expect to see, so I want to keep the prompt open-ended.