I actually applied for a job with those well regarded german contractors as Edinburgh Tram design manager about 18 months ago. In hindsight I was bloody lucky that I didn’t get it.
It does go to the Airport and it does stop outside Waverly and through Haymarket.
Just as an aside – I was working for Network Rail when the Scottish Parliament cancelled the Edinburgh Airport Rail link – which we had spent a shitload of time and effort developing. It would have provided a link from Dundee, Stirling, Glasgow etc directly to the Airport and then on to Edinburgh. It was cancelled for no good reason other than they were already comitted to building the Tram.