You need two steps for this.
The first step is doing a reverse geocoding call to Nominatim, OSM's most popular geocoding service. Be aware that OSM's official Nominatim instance has a rather strict usage policy because it runs on funded servers. But you can use MapQuest's Nominatim instance as an alternative and even install your own instance. Because Nominatim only stores the post-processed data it doesn't have any information about the original tags.
The second step is extracting the osm_type
(which is the type of the element and can be either node
, way
or relation
) and the osm_id
(which uniquely identifies the element) from Nominatim's result. With these information you have to make a call to the OSM API to get all information about the corresponding element. This includes all tags.
Note that there is a similar Question&Answer platform for OSM which allows you to reach a much larger part of the OSM community.