What's the method of subsidy there? Contributing to Airbus shares?

Commercial aviation fuel is tax exempt in the EU, I would already count that as a subsidy (yes, I count not taxing something that's normally taxed as a subsidy, even if it isn't done by directly paying out money).

Subsidising airports and fuel, presumably.

How is it subsidized while a local flight costs more than an international one?

The idea is to push people to use the train, but a train isn't an alternative if it takes 9 hours compared to the 2 hour flight.

ICE from Hamburg to Munich is about 5 hours. That's basically the other end of the country. Not sure where 9 hours come from.

And your 2 hour flight easily goes to 4-5 hours if you add the security theatre and the extra overhead that transport to/from the airport entails. They are far outside the city whereas central stations are usually in the city center.