What an interesting way of looking at acidity! How I would look at it would be the more standard way which is to compare the stability of their conjugate bases...
The ethanoate ion has an methyl group, which is electron-donating, donating electron density towards the oxygens, concentrating the negative charge. This makes it a more unstable conjugate base.
In stark contrast, the methanoate ion, does not have the electron donating group and thus, does not have such a high concentration of negative charge. This makes it the more stable conjugate base.
The explanation proposed can also explain the differential solvation of the two carboxylic acids...
With a higher charge density, ethanoic acid would form a more "ordered" hydration shell as the electrostatic attraction between the water molecules and the negative charge is greater.
With a lower charge density, methanoic acid would form a less "ordered" hydration shell as the electrostatic attraction between the water molecules and the negative charge is not as great.
Consequently, the decrease in entropy for the dissociation of ethanoic acid is much greater than that for the dissociation of methanoic acid.
Therefore, the dissociation of ethanoic acid would be less favoured than the dissociation of methanoic acid, based on both considerations of entropy and conjugate base stability, which are actually linked.