does the new apple watch 3 support spotify?

You're welcome! 🙂

I'm afraid that no-one here can tell you anything about Apple's or Spotify's unannounced plans and it is not allowed to speculate here. You are not talking to Apple here - this is a user-based technical support community.

Hi

Spotify does not currently offer an app for Apple Watch:

Spotify Music on the App Store

If you would like Spotify to do so, then you may wish to submit a feature request to them.