There are two parts to Mopidy-Spotify.
- libspotify: provides playback + lookup (and few other things). Requires premium account. Auths with your username + password
- Spotify Web APi: provides everything else. Auths with client id and secret.
Your log shows libspotify login is unable to contact the server (which is different to the Web API server). If I remember correctly, libspotify uses https://apresolve.spotify.com/ to get a list of nearby servers it can use. Sometimes some of those servers have issues - perhaps this is another case of that. I’ve heard from elsewhere that ap-gew4.spotify.com is currently broken but usually Spotify resolve these issues after a while. Or you could try forcing it to use a specific server by setting an entry in your /etc/hosts file like:
104.199.65.124 ap-gew4.spotify.com
Where 104.199.65.124 is the IP of one of the other access points that were provided to you from apresolve.spotify.com
Or you have some kind of firewall in place?