Given that right now Twitch doesn’t provide a way to store configurations Twitch side, you need to do the oAuth dance and store the oAuth in your EBS anyway.
You should be able to redirect a user to Spotify from the configuration panel of the extension, or open a popup (again from the configuration panel) that does the relevant dance.
For example:
Which for my extension takes you to:
From here you should be able to send people round the Spotify oAuth loop.
Said page is configured here:
And don’t forget the whitelist under Ext. Capabilities:



