I am using https://nominatim.openstreetmap.org/search and it seems that some queries aren't returning postcode inside of address object for some reason and others do.
For example:
https://nominatim.openstreetmap.org/search?countrycodes=us&addressdetails=1&format=json&q=47711
returns the postcode, but this does not:
https://nominatim.openstreetmap.org/search?countrycodes=us&addressdetails=1&format=json&q=evansville
Evansville has more than one postcode. Which one should nominatim return? 47711 is just one part of Evansville, but Evansville has many more postcodes.
A postcode can only be returned if it is exact as in one postcode for the query.
So e.g. if you query the North High School in Evansville as in here: https://nominatim.openstreetmap.org/search?countrycodes=us&addressdetails=1&format=json&q=north%20high%20school%20evansville you'll get a postcode.