OK, I've figured this now. Spotify is evil and recently has started blocking everything unless I'm a registered company with 250k MAU and go through their process. It's so great that they don't tell you this before you wasted time making your app and everything appears to work ok with your own account.

But, well, I can still manually whitelist your Spotify email beforehand then it should work.

If someone else wants it please let me know your Spotify email here or via DM.