Places searches can you run beyond a proper City name? is it all - aside from the image text read results - being tied to a latitude and longitude that is embedded in the photo?
Yes, it is completely dependent on the embedded location data (long/lat) in the photo itself. What results that returns—a city, a region, a specific location (like a restaurant or building)—Depends on how Apple's heuristics interprets that location data, and how closely you are zoomed into the map. Wide zoom resolves general locations, zooming in resolves more specific locations.
For example: You're on vacation in Seattle, and go have a nice dinner at Anthony's. You take several pictures of your meal. Apple location data may (or may not) recognize that those photos were taken while at Anthony's. After dinner, stuffed, you take a walk down the pier and keep taking photos. You're not still at Anthony's, but depending on the location data your photo attaches to the photo, the heuristics may still indicate the photo was taken at Anthony's. Or they may just generically say Pier 66, Seattle. You could then manually edit the location data of the photos to indicate an exact location, separating the ones that were taken while you were having dinner, and the ones taken while you were on your walk.
Or, as you've already noticed, you may take a picture of your menu and on that menu are the words "Anthony's Pier 66, Seattle". Searching for Seattle would find that photo regardless of its location data because it is able to search intelligently for words in photos (as others have noted) on any modern iPhone, iPad, or Mac.
This Apple Knowledge Guide article explains broadly how to view locations (on a Mac).
This Apple Knowledge Guide article explains how to manually change that location data (among other things).
How any of this works in Aperture is an unknown because Aperture was developed (and abandoned) before any of these heuristics or machine learning-based systems existed. As I mentioned in your locked thread, it is not relevant to this conversation in 2024.