Spotify does not directly support playing music on your Apple Watch, beyond a remote control app for Spotify app on the iPhone.
As Spotify is not an Apple company, you will have to ask Spotify when they will support the Apple Watch.
In the mean time these 2 articles may help you:
https://www.wareable.com/apple/how-to-use-spotify-on-apple-watch-6609
https://www.ondesoft.com/spotify-converter-for-mac/play-spotify-music-on-apple-watch-without-iphone.html
NOTE: the article is slightly out of date, as watchOS 6 does allow 3rd party streaming; Pandora is offering Apple Watch LTE streaming.