Hello, the roads through Fredericksburg were correctly assigned their classifications per this classification page: https://wiki.openstreetmap.org/wiki/Virginia/Highway_classification

Per the document, as well as the broad US highway classification guidelines, roads are classified based on their connectivity to places and other roads and importance in the road network. Since Route 3 BUS and US 17 BUS connect their respective mainline highways to the downtown area, primary would be the best classification for these routes. While they may appear to be residential roads as they have houses along them and a narrow, low speed construction, highway=residential is only used on streets that are used almost exclusively for accessing neighborhoods or other small streets, while William Street in particular links Route 1 and 3 and I 95 to Downtown Fredericksburg, 17/2 Business plays the same role here, linking the Downtown to the Route 3 bypass and down towards mainline Route 17 and eventually Route 301.

Traffic also plays a role in highway classification (in cooperation with other criteria). Per this map (https://www.arcgis.com/apps/mapviewer/index.html?webmap=bff29e1bc0fd4908b2c035fe67695088), William Street sees 11k average daily traffic while a true residential street in the area will see only about ~1k AADT.