The general term seems to be "mouth resonator instruments", but this is an informal rather than a taxonomic term. In addition to the Jew's harp and nose whistle, there are various mouth-resonated string bows (Britannica: Mouth Bow; SoundsOfAngkor: Mouth Resonator Fiddle))
It should be mentioned that the oral cavity is not the primary resonator for the Jew's harp. The Jew's harp is an idiophone, meaning that the entire instrument resonates and is the primary producer of the sound. Although the mouth amplifies and modifies the sound, it's the instrument itself that produces it.
The jew’s harp is one of several idiophones (instruments whose sounding parts are resonant solids) vibrated by plucking rather than by percussion. (SOURCE: Britannica.com)
idiophone: an instrument the whole of which vibrates to produce a sound when struck, shaken, or scraped, such as a bell, gong, or rattle. (SOURCE: Oxford Languages via Google Search)
More specifically, it's a lamellophone, a subset of idiophones.
A [lamellophone] may have a single tongue (such as a Jew’s harp).... (SOURCE: Wikipedia)
This makes the Jew's harp distinct from the nose whistle (and nose flute), which is an aerophone, in which vibrating air is the primary means of sound production.