Soft transpositions made of songs within a playlist are saved to that certain playlist.
The saved Soft transpositions are independent and that allows for a song to appear in different playlists with different transpositions.

Although set in a specific key (set in editor info; see hard transposition), if necessary, the same song can show independently in any appropriate key in different playlists (and in the song index).

When you soft transpose a song, it only transposes that song in that location (playlist or song index). For different bands and backing various singers, once you soft transpose the key, it is remembered in the relevant playlist.