It is only exchange-value that is significant under commodity production and exchange, because it determines how many use-values the producer can obtain from the exchange/sale of their commodities. It is not that society, or the individuals within it, are no longer interested in consumption/use-value, and seek to maximise it for the least expenditure of labour, but that the means of achieving that are now changed. Each commodity producer, now, seeks to obtain more use-value for less expenditure of their own labour, i.e. to obtain more labour for less.
The way of achieving that is to raise the efficiency of their production above the average, to reduce the individual value of their own production below the market value. In turn, this process, which creates winners and losers, brings about a differentiation into bourgeois and proletarians, and a development of capitalist production. But, this capitalist production, as Engels describes in his Supplement to Capital III, also, brings about a further change in the form of manifestation of The Law of Value. Under generalised commodity production and exchange, it manifests in the form that commodities exchange in proportion to their market-value, but under capitalism, that is no longer the case. Under capitalist production, they exchange at prices of production.
Under generalised commodity production and exchange, commodities exchange at their values, i.e. at their market value, and, in a money economy, at their market price. However, once capitalist production begins, the capitalist is primarily concerned with maximising their annual rate of profit, on the capital advanced. As the organic composition of capital, and rate of turnover of capital varies, for different types of commodity, the annual rate of profit is different in different spheres of production. Consequently, capital accumulates more rapidly in those spheres of production where the annual rate of profit is higher. Supply in those spheres rises relative to demand, so that the market price/price of production in these spheres is lower than the exchange value of the commodity, and vice versa.
But, as Marx and Engels set out, although this means that, under capitalism, the allocation of labour to production of different commodities is no longer determined by the value of those commodities, as occurred previously, but, now, by the requirement to maximise the annual rate of profit, that does not mean that The Law of Value ceases to operate under capitalism. It is simply that its form of manifestation is different. Taking production as a whole, the total prices/prices of production are equal to the total of values. The fact that, with a given quantity of labour, only a given quantity of use-values can be produced, determined by the labour-time each requires, continues to apply.
“At the same time it goes without saying that the laws which are valid for definite modes of production and forms of exchange also hold good for all historical periods to which these modes of production and forms of exchange are common. Thus, for example, the introduction of metallic money brought into operation a series of laws which remain valid for all countries and historical epochs in which metallic money is a medium of exchange.” (p 187)
As Marx sets out in A Contribution To The Critique of Political Economy, money arises, naturally, out of the production and exchange of commodities. The very process of repeated exchange of a growing range of produced commodities, leads to the use of just one of these commodities to act as an indirect measure of the value of all other commodities. This commodity becomes the money commodity. To perform this function, its own value, i.e. the labour-time required for its production, must be well established, and the commodity must be widely traded. As Engels sets out, cattle were, therefore, used widely as such a money commodity. But, they suffer numerous defects. Many of those defects are removed by using precious metal, such as silver and gold as the money commodity.
Again, Marx sets out the laws relating to the use of precious metal as the money commodity, in A Contribution To The Critique of Political Economy, and, on that that basis, he sets out the modification of those laws that arise from the subsequent use of metal and paper tokens, as currency, which have their own laws of motion.



