I’ve dug a little deeper and discovered that most of these issues are rooted in OpenStreetMaps.
the crazy idea to include Stephansplatz subway station with routable paths is actually already implemented in OpenStreetMaps
completely unbeknownst to me there’s a long distance trekking route called “Sultan’s Trail” (kind of a knockoff of Camino de Santiago) that apparently runs from Vienna to Istanbul. Somehow this trail has made it into OpenStreetMaps with a really high routing weight, so all routing apps seem to follow it, and it doesn’t run straight through Kärntnerstraße, but takes the detour shown over Neuer Markt.
Doesn’t make the routing in the Suunto app any better, but at least Suunto is not alone to blame here.