Not directly, and we agree the workaround is clunky. Spotify only lets an app connect up to five users unless the developer is a company with 250,000+ monthly active users, so SetListr can't offer one-tap Spotify playlists the way it does for Apple Music.
Until that changes, open a setlist's ⋯ menu and choose Copy Song List or Export as CSV, then paste or upload it into a free transfer service such as TuneMyMusic or Soundiiz to build the playlist in Spotify (or YouTube Music, Tidal, Deezer and others). How to Import… in the same menu walks you through it. For a single song, long-press it and choose Search on Spotify.