I want to change a feature type to Driveway, but while I can see this feature type on existing features, it does not seem to be available to select in the iD editor. (Listings under Minor Roads are: Minor/Unclassified Road, Living Street, Residential Road, Service Road, Track / Land-Access Road).
“Driveway” is just one of thousands so-called presets available in iD (actually, they are imported from a sister project “iD tagging schema”). Every preset has a name, icon, and a number of predefined tags, some of which are just “subtags” of a “major” tag. For example, there’s the general preset “Service Road” (highway=service), and presets for its more specific subtypes such as “Driveway” (adding service=driveway) or “Parking Aisle” (adding service=parking_aisle).
As you discovered, only a small subset of presets is available by browsing the “directory”. As Minh said above, the most efficient way to locate a desired preset is by typing a keyword in the search bar. Search is actually quite smart, since it also finds presets with synonymous or related names with the search keyword.