Even when casting from a playlist, just skipping to the next track can cause a disconnection with the awful "your Spotify account is being used on another device." Nothing is guaranteed when it comes to connecting Spotify to Chromecast. Only that you'll have problems.
Okay. Not sure it really solves all of it. But it seems (careful!!) to work out fine with me.
So, I removed the Spotify app from my Galaxy S6 (yes, a bit old :-(). And downloaded it again from the Play Store. Still some albums don't play. Deleting the album using my desktop Spotify login and then searching the album and storing it again enables me to cast it again. Still got the feeling something was wrong al the way, and deleting this 'memory' gets rid of the problem.
I've found that going into Google Home app on your phone and then clicking on the 'Device' and then clicking 'Cast my audio' will "mirror" the audio. "Mirroring lets you cast your phone's or tablet's screen and audio to your TV or speakers." This is an unacceptable hack as far as I'm concerned and I'm not sure if the audio is of the same quality. Something broke. Spotify are the mechanics. If I could download a spreadsheet of my Spotify library I'd be heading over to Amazon Music in a heartbeat. I'll wait a short time to see if Spotify can resolve the issue and continue using Amazon Music's free three month trial. The clock is ticking.
It's ridiculous that this is still going on. Still can't cannect to any cast device to play songs saved in my library. Songs not saved work fine. Yes, Spotify opened an "ongoing issues" thread but have then completely ignored it.