How do I eager load a dropdown field?
Dropdowns are not relations, and therefore they don't need to be eager loaded (and indeed can't be eager loaded).

Here's an explanation of what's going on under the hood with eager loading: Speed up your Craft CMS Templates with Eager Loading

TL;DR only things that are relations, which are other Elements are candidates for eager loading. Other fields like Dropdowns, etc. are loaded as part of the content already.