The audio behavior is always a little funky on macOS, for the specific steps given I think the problem is that the 'play' button on the keyboard is more like a

The audio behavior is always a little funky on macOS, for the specific steps given I think the problem is that the 'play' button on the keyboard is more like a 'resume' button really, which can cause it to do seemingly bizarre things if you haven't been doing any audio recently. I would expect that if you clicked play in Spotify, then pause, then hit the key on the keyboard it should behave.