How do you establish an area in which to search (restaurants, for example) for Maps.app
It’s simply a limitation of Apple Maps.
To find places around a certain area, Apple touts the “Nearby” feature supposedly which allows you to find points if interest nearby your current location.  If I search “pizza near research triangle  park, nc” it gave me pizza places near the closest city center to me - downtown Fort Lauderdale, FL.
I tend to use Bing Maps as my preferred tool followed by Google. I did the same search  in Bing and the search area was as you described - bounded by the visible area in the window. If I zoomed or panned the map, the results  adjusted accordingly.
I have found that 3rd party apps “force” Google maps regardless of what you want as your default - I suspect it’s to ensure a consistent and rich user experience.
While I’d love to recommend the native tool, I can’t.  I'd use the tool that meets your needs.