In short—the community and your own personal judgement. 

The rules are really just vague guidelines that are followed by local OSM communities or individuals who try to put two-and-two together based off how everyone else does it. For US road classification specifically, these are based upon a community-built, consensus-approved documentation like this OSM Wiki page: https://wiki.openstreetmap.org/wiki/United_States/2021_Highway_Classification_Guidance

For primary roads in urban areas in particular, the guidelines would be to use this classification on the most important arterial roads—which is vague, and up to interpretation. Prior to when I started editing, a lot of the Las Vegas Valley's primary roads already followed this guideline. If I can recall correctly, the original significant primary roads in the valley were Craig, Lake Mead, Charleston, Tropicana, Boulder Highway, Las Vegas Blvd, Rainbow, Rancho, Paradise, Eastern, 5th Street, and Nellis—some of the most important arterial roads in the area at a glance. I went off how these were classified and upgraded other secondary roads, like Durango, Sahara, Cheyenne, etc. up to primary based on their similar roles and characteristics (like connectivity with major highways and regions of the valley, AADT, physical construction, road designation, HGV route) etc.

Unfortunately, a lot of highway classification cannot be determined with a source or a road number, and it will have to be up to the opinions of one, two, or many mappers. This can be avoided with a state highway classification page, but as far as I know, Nevada doesn't have one (yet). For the mean time, discussing and scrutinizing each road with other mappers one-by-one may be the best way to go about it.
