Yes but that's not a solution it's a workaround. The nuts and bolts of the issue is that you can connect when playing songs/albums via search but cannot connect when playing the same songs/albums from the library.
It's very clearly an issue with the library and personally I'm getting fed up with waiting for a fix.
I urge everyone with this problem to contact support and insist on a refund of their premium subscription to hopefully generate some visibility to those higher up the food chain than @peter who seems to have gone to ground after initially seeming interested in solving this problem.
I have found that if I connect before playing a song it seems to work OK, but does not work if I already started the song on my phone first. If it hangs my workaround is to select a different device like a TV or stereo, then go back to the chromecast device.
I've been testing Spotify for about 6 weeks now and I find it to be incredibly frustrating when working with Chromecast devices. I have several Google Home speakers and speaker groups setup in my house. Spotify randomly/frequently disconnects/stops, will sometimes connect to speakers I did not specify (either by voice or app), and will not play on speakers I select (via app or browser). Basically, everything pretty much everyone on this thread has commented on. Hope this can be fixed soon as all of the other music apps I use DO NOT have this issue.
I have found that songs that have been downloaded for offline playing in a Spotify playlist have the most issues when trying to use Chromecast to my Google Mini speakers.
Streaming songs directly from the Internet over Spotify seem to work just fine.
Problem is, i'm not sure if there is a way to fix this now. I have certain playlist that have been downloaded (so i can listen offline on airplanes while traveling) that are now local on my device. Not sure how to "un-download" these.
EDIT: iPhone users can remove the download of playlist (mostly?) by going into the playlist and at the top of the list moving the Download slider from green to gray. Alternately, tapping the 3 dots menu at the top right then selecting "Remove download".
The best case scenario would be for this problem to get fixed between Google Chromcast and Spotify directly.
iPhone X IOS 13.3.1 Spotify Family Google Mini (Gen1 & Gen2)