The entropy of a photon gas in equilibrium (emitting e.g., black-body radiation; BB) is
$S \propto V \cdot T^3$
where $V$ is the volume and $T$ is the temperature of the gas [see https://en.wikipedia.org/wiki/Photon_gas].
Now, in case of a BB, $T$ is linked to the peak frequency of the BB, $\nu_{\rm peak}$, according to the Wien's law:
$\nu_{\rm peak} \propto T$
[see https://en.wikipedia.org/wiki/Wien%27s_displacement_law].
So, the entropy of a BB in a unit volume is proportional to the to the third power of peak frequency:
$S \propto \nu_{\rm peak}^3$.
Thus, from this I understand that, for instance, a BB radiation peaking at visible wavelengths (like the Sun) would have higher entropy than a BB radiation peaking at infrared wavelengths (like the Earth).
However, this looks in contradiction with many arguments saying that the Earth is "powered" by low-entropy photons coming from the Sun, which are absorbed and then irradiated as high-entropy infrared photons [see e.g., https://www.preposterousuniverse.com/blog/2016/11/03/entropy-and-complexity-cause-and-effect-life-and-time/].
Where am I getting wrong?