Seems that newest linux spotify client checks online status reported by network manager. This status can be separately checked with "nm-online" tool. If tool reports [online] then spotify app works. If it reports [offline] then spotify "blindly" says offline (despite connection working perfectly).
There can be many reasons why NetworkManager thinks connection is offline. Seems that the majority of people here have problems with connectivity check. My problem was that connections were not managed by network manager, but by separate tool (netplan).
Hopefully linux desktop app will be changed back to ignore connection status reported by network manager.