Doing some research on what data-consumers might be expecting…
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Nominatim’s Proper support for postal towns in the US #1120 – From the discussion it sounds like Nominatim is actually doing area search for boundaries to find a matching “city”.
Or maybe only if addr:city isn’t specified? I’m not sure.
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OSMAnd doesn’t have an issue related to this exact problem, but US/Canada Addresses - not found #18924 and some testing seems to show that it does an “enclosed in” boundary search rather than looking at addr:city