There are direct EC and some ICE trains between Munich and Innsbruck.

Well, in normal times. I have a reservation on the ICE from Innsbruck to Munich on Saturday. At the moment the DB website is both claiming that the direct trains are running, and that there are problems at Kufstein and I will have to use a combination of Innsbruck's S-train and a Bavarian regional train to get between the two. I am reminded that Schrödinger was Austrian and perhaps I will simply have to embrace the duality of the dead-and-alive railway in his home country.