You have an invalid assumption that extra power is spent on better compression or decompression. It generally takes less energy to decompress a better-compressed file, because the decompression work is mostly proportional to the file size. Energy for compression varies greatly depending on codec and settings, but JPEG XL is among the fastest (cheapest) ones to compress.

Secondly, you have an invalid assumption that the amounts of energy spent on compression have any real-world significance. Phones can take thousands of photos when working off a tiny battery, and most of it is spent on the screen. My rough calculation is that taking over a million photos takes less energy than there is in a gallon of gas.

Apart form that, compression cost is generally completely ignored, because files are created only once, but viewed (decompressed) many many times over.

Smaller files save storage space. Storage has costs in energy and hardware.

Smaller files are quicker to transfer, and transfer itself can be more energy intensive than compression. It's still small in absolute numbers.