As I know, Spotify doesn’t support Pod Nano, Classic, or Shuffle. But it is still possible to listen to Spotify music on the old generations of iPod Touch by using a little trick.
And this is how I listen to Spotify songs on my iPod Shuffle. First, install the Spotify Converter on your computer. Then use it to download music from Spotify into the local folder. Last, move the local Spotify tracks to your old iPod Touches. These local Spotify tracks are playable without the Spotify app.
You can refer to this article to get more details: https://www.audkit.com/spotify-music/spotify-to-mp3.html