Played the game normally, had small issues and tried to restart client. That was a BIG mistake…
First “purchase”. On second try “install” (with greyed-out button).
Clicked on non-horizons version and back on full – get “play” button. Client started.
Now I finally can see orange square with “logging in” header. Seen something appeared for a fraction of second before, now I have a chance to see it in detail.
UPD: Just logged in. Everything seems to work normally.