The point obviously isn't to give grocery stores more money for no reason, it's to support products that have higher quality standards.
Take poultry as an example, standards vary by county, but the differences between quality labels can be stark. Cheap poultry is often raised in tiny indoor cages and they need to be pumped full of antibiotics due to the unhealthy living conditions. On the other end of the spectrum, organic poultry is free to roam in fields and the coops are regularly moved or kept clean, avoiding the need for antibiotics in the first place.
Even if you disagree that the latter provides a better quality product, it's pretty clear that supporting brands with higher standards results in better living conditions for the animals.
If an animal product is more expensive at point of sale it does not also follow that the producers of said product provided better living conditions for their animals. It could be that the producers of the cheaper of two similar products provided better living conditions. Again, you have the causation all mixed up.
All else being equal, providing betting living conditions should increase the cost to the farmer. But thah A implies B does not mean thah B implies A. Not everything thah increases production cost is better animal living conditions.
And even if I bought the more expensive animal products it would also not in any way affect the animal's living conditions.
The price of an animal product in no way affects the way the producer treats the animal. You have the causation completely backwards.