After this working fine for a long time (mostly -- the occasional weirdness did occur), this morning I discover I can no longer successfully connect Spotify properly with my Chromecast. Interestingly, it does start playing the music, but it still says connecting and then gives up as though the connection was never established. The music keeps playing, but I can no longer interact with it.
I have rebooted the Chromecast and my phone, and my phone is a brand new Pixel 2 (i.e. up to date). I was able to cast from Netflix, so it would appear that the problem is specific to Spotify.