My Misconception of Entropy
The association of entropy with disorder is anthropocentric. &quot;Disorder&quot; is a concept derived from our experience of the world. The association with &quot;disorder&quot; is clearer once we explain what we mean by &quot;order&quot;. The following definition among those provided by Merriam-Webster most closely fits the intended meaning:

a regular or harmonious arrangement

Since regularity always implies lower entropy, all else being equal, it is therefore fair to associate &quot;order&quot; with lower entropy.
The association with &quot;order&quot; or regularity also syncs with the concept of entropy according to Boltzmann's statistical mechanical definition ($S= k_\mathrm B \log \Omega$). $\Omega$, the number of microstates available to the system, can be quantified using the entropy. More possible unique microstates implies a higher entropy. Greater regularity implies more constraints regarding arrangement of the system and therefore less possible microstates. Solids are usually more regular and therefore have lower entropy than fluid states at the same T. Same when comparing gases and liquids. The possible microstates increases from solid to liquid to gas.
This also jives with the informational-content definition. You can use less information (use a more compact description) to describe an orderly (regular) system. You need more information to describe all possible arrangements of molecules in a gas or liquid than in a solid. Think of entropy as measuring the length of the recipe required to build all possible arrangements of the system.