I've been having the same issue for about a week now. It has impacted all 5 of the Roku boxes in my home, as well as a single FireTV set top box. In each case, the app would open to the Spotify logo, but the app would never fully load. The issue did not impact the Spotify app on my mobile phone regardless of whether I was connected to my home network or my mobile carrier.
While troubleshooting, I actually connected one of my Roku boxes to the Internet via the hotspot feature of my mobile phone, and the Spotify app opened and ran just fine. This pointed to either an issue with my home Internet Service Provider as compared to my Mobile Service Provider, or an issue with my local network configuration. After several hours of troubleshooting, I was able to isolate the issue to the IPv6 setting in my home router. My mobile phone hotspot has IPv6 enabled by default, whereas I had this setting disabled on my home router. Once I togged IPv6 setting in my router to enabled, the Spotify app started working on all the devices in my home.
Not sure why this made a difference, as the Roku Box itself appears to be using IPv4, but apparently Spotify recently updated something in their set-top box app that requires IPv6. If you are having similar issues, try enabling IPv6 in your router to see if it helps.