I would recommend using the flatpak instead. The Third Party section of the software center will be going away in the future.
This particular problem seems to be due to Spotify servers.
If you wish to continue using the Third Party section while it exists, you can try installing it via the command line. It should at least provide immediate feedback.
sudo eopkg bi --ignore-safety https://raw.githubusercontent.com/getsolus/3rd-party/master/multimedia/music/spotify/pspec.xml
sudo eopkg it spotify*.eopkg;sudo rm spotify*.eopkg