You got lucky, i just happened to be looking for this an hour ago.

You can use the data from Global Human Settlement dataset Settlement Grid:
https://ghsl.jrc.ec.europa.eu/datasets.php

Its a gridded raster tif where each pixel has a value for urbanization. If
you load it into qgis and use some python, you can classify an input set of
points if they are urban or rural.

Dont know if theres a ready API already available that already offers this
as a service.

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