I think it’s a fairly straight forward tagging situation. I tag the place_of_worship using either a closed way or node as appropriate, then I tag the stupa as a node or closed way with man_made=tower and tower:type=stupa. In other words I’m tagging the stupa as a structure only and not ascribing any other significance to it. If it sits atop or is part of a place_of_worship, or a monument, so be it. Use a node or a closed way for either, or both, structures. The two major tags are not mutually exclusive because at top level one is an amenity and the other is man_made.
I’m in the process of working out a Garmin icon for stupa with the Lambertus folks. Hopefully we will end up with something for OSM as well.