There has been a long discussion in the neuroscience community how neuronal firing encodes information. The two extremes of the proposed solutions are temporal coding and rate coding, but there are intermediate positions such as held by the parent poster (and myself, and nowadays most other people that care about this niche).
Wikipedia is decent-ish on the topic: https://en.wikipedia.org/wiki/Neural_coding
Wulfram Gerstner's book has a nice discussion of the theory and limitations of different proposed coding schemes, which might interest the technical audience here. In particular, I think the parent poster alluded to the ideas presented in the last section here: https://neuronaldynamics.epfl.ch/online/Ch7.S6.html
Really and truly this "discussion" should have been put to rest a long time ago.
Neurons encode information with the temporal precision needed to encode that information. Since most objects are somewhat permanent, the temporal precision can be very low, yielding effectively a rate code. For tasks for which the (relative) timing is critical, e.g. the encoding of auditory sequences, the temporal precision of the neural code is high, yielding effectively a temporal code. Some problems are neither here nor there, in which case the neuron will encode as much information as possible at a low rate / temporal resolution, and then encode diminishing amounts of information at successively higher temporal resolutions (the Fourier code alluded to by the parent poster). Higher temporal precision typically requires more control, larger circuits, and hence more energy expenditure.
Bill Bialek's group had a paper that quantified the amount of information present in a visual neuron of the fly at different temporal resolutions (/frequencies) as early as 2008: https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...