A simple option would be weather_control=launchpad, to distinguish from (orbital) "transport" launchpads ("aeroway"), similar to military=launchpad.
Further possible tags to refine it :
"suborbital" for type and "anti_hail" for rocket launch
https://taginfo.openstreetmap.org/keys/launchpad%3Atype
https://taginfo.openstreetmap.org/keys/rocket%3Alaunch

The same principle could also be used for balloons (balloon:launch:=*), either weather_control=launchpad or tourism=launchpad. This way you could filter for any of the parameters (weather, suborbital, rocket or balloon). And especially distinguish from "aeroway" (even without "additional tags").

There weren't any other suggestions so far : https://wiki.openstreetmap.org/wiki/Talk:Tag:aeroway%3Dlaunchpad

Other ideas ?