Well, well...
So today they have restored the server connection, so the app can connect again. Since the upgrade wipes local storage, it first needs to resync before the old trips can be shown.
However, the new function - booking flights from app without re-login - does not work.
When you hit "Book a flight" it is supposed to work by swapping to your browser and sending you to the website, where it first logs you in and then serves you the book a flight form.
But the magic log in link does not work, it just hangs safari. After the request times out, you can hit the log in button yourself and type in details. Which is exactly like it worked before the update.