Hi Jordan. There's not really a clear consensus when it comes to classifying urban roads within the United States. https://wiki.openstreetmap.org/wiki/United_States/2021_Highway_Classification_Guidance details the rural classification system well, but has not been updated with urban guidelines yet. I have not contributed to the MN-specific page myself at https://wiki.openstreetmap.org/wiki/Minnesota/Minnesota_highway_classification, but it also deals more with rural classification rather than urban.

What I generally look for in urban areas is a combination of road quality (e.g. number of lanes, pavement, turn lane presence), importance to the network as a whole, and traffic counts. I'll use the examples of north/south routes in the Macalester-Groveland area, and why they might be classified in such a way:

Snelling is the only road in the area that is consistently at least two lanes in each direction, and provides the most major access to the entire area from the rest of the metro area via I-94. So primary makes sense for it. And as for Cretin north of Lake I'd view it as primary as well, since it's the main route from the east via I-94 into the southeastern Minneapolis areas in combo with Lake Street.

The rest of Cretin, Fairview, and Lexington are the ones I'd view as secondary roads. These provide access to the area from other freeways in the area. They're clearly less major routes than Snelling in the area since they only have one lane in each direction and not quite as much traffic, but they still have significant traffic and serve important connections into and out of the area. Hamline north of Ayd Mill is important alternate route between I-84 and I-35E for when the Snelling/Selby intersection inevitably backs up, so that's why I'd put it as secondary as well.

Mississippi River Blvd, Cleveland, and the rest of Hamline are much less important. They don't serve any regional connections into and out of the area, instead only serving local traffic. So that's why I'd keep these at tertiary.

Let me know if this helps at all for why I see the roads in the way I do.