In OpenStreetMap, you can zoom in close … right click … Query features → this will update the left column & at the bottom it will display the list of Relation records that enclose what you right clicked
I often do this to figure out which street a city is in
Your Cooktown node link is interesting, because right clicking any of the three visible cities & choosing Query features results in it showing me that the streets all exist in Herndon
On the other hand, right clicking Kinross Circle shows me that it’s not in any city - just the county.
This is a typical issue where cities don’t exist in OpenStreetMap. Adding a City to OpenStreetMap is quite a process